@article{ author = {Abbasi, Naser}, title = {Generalized Mappings Related to Hermite-Hadamard Inequality}, abstract ={In this paper we introduce two new mapping in connection to Hermite-Hadamard type inequality. Some results concerning these mappings associated to the celebrated Hermite-Hadamard integral inequality for preinvex functions are given.  }, Keywords = {Hermite-Hadamard inequality, invex sets, preinvex functions}, volume = {3}, Number = {1}, pages = {1-13}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.1}, url = {http://maco.lu.ac.ir/article-1-95-en.html}, eprint = {http://maco.lu.ac.ir/article-1-95-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Nazari, Abdollah and HeidariTavani, Mohammad Reza and Mombeini, Esmaeil}, title = {Existence of at least one non-trivial periodic solution for a class of ordinary p-Hamiltonian systems}, abstract ={Based on recent variational methods for smooth functionals defined on reflexive Banach spaces, We prove the existence of at least one non-trivial solution for a class of  p-Hamiltonian systems. Employing one critical point theorem, existence of at least one weak solutions is ensured. This approach is based on variational methods and critical point theory. The technical approach is mainly based on the at least one non -trivial solution critical point theorem of G. Bonanno.}, Keywords = {Multiple periodic solutions, Hamiltonian systems, Critical point theory, Variational methods.}, volume = {3}, Number = {1}, pages = {15-22}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.2}, url = {http://maco.lu.ac.ir/article-1-102-en.html}, eprint = {http://maco.lu.ac.ir/article-1-102-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Babayar-Razlighi, Bahman and Soltanalizadeh, Babak}, title = {Application of Differential Transformation Method to the Dullin-Gottwald-Holm equation}, abstract ={‎Nonlinear problems in partial differential equations are open problems in many field of mathematics and engineering‎. ‎So associated with the structure of the problems‎, ‎many analytical and numerical methods are obtained‎. ‎We show that the differential transformation method is an appropriate method for the Dullin-Gottwald-Holm equation‎ (DGH), ‎which is a nonlinear partial differential equation arise in many physical phenomenon‎. ‎Hence in this paper‎, ‎the differential transform method (DTM) is applied to the Dullin-Gottwald-Holm equation‎. ‎We obtain the exact solutions of Dullin-Gottwald-Holm equation by using the DTM‎. ‎In addition‎, ‎we give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations‎. ‎These results show that this technique is easy to apply and provide a suitable method for solving differential equations‎. ‎To our best knowledge‎, ‎the theorem presented in Section 2 has been not introduced previously‎. ‎We presented and proved this new theorem which can be very effective for formulating the nonlinear forms of partial differential equations‎.}, Keywords = {Dullin-Gottwald-Holm equation, Differential Transformation method, Spectral method.}, volume = {3}, Number = {1}, pages = {23-35}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.3}, url = {http://maco.lu.ac.ir/article-1-99-en.html}, eprint = {http://maco.lu.ac.ir/article-1-99-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Farhadi, Hami}, title = {Characterizing Left or right centralizers on $ star $-algebras through orthogonal elements}, abstract ={In this paper we consider the problem of characterizing linear maps on special $ star $-algebras behaving like left or right centralizers at orthogonal elements and obtain some results in this regard.}, Keywords = {Left centralizer, right centralizer, $ star $-algebra, orthogonal element, zero product determined, standard operator algebra}, volume = {3}, Number = {1}, pages = {37-41}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.4}, url = {http://maco.lu.ac.ir/article-1-98-en.html}, eprint = {http://maco.lu.ac.ir/article-1-98-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {MOORTHY, C. GANESA and SIVA, GURUSAMY}, title = {Automatic Continuity of Surjective Almost Derivations on Frechet Q-Algebras}, abstract ={In 1971 R. L. Carpenter proved that every derivation T on a semisimple commutative Frechet algebra A with identity is continuous. By relaxing the commutativity assumption on A and adding the surjectivity assumption on T, we derive a corresponding continuity result, for a new concept of almost derivations on Frechet algebras in this article. Also, it is further proved that every surjective almost derivation T on non commutative semisimple Frechet Q-algebras A with an additional condition on A, is continuous. Moreover, an example is provided to illustrate our main result.}, Keywords = {Almost derivation, Automatic continuity, Frechet Q-algebras.}, volume = {3}, Number = {1}, pages = {43-48}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.5}, url = {http://maco.lu.ac.ir/article-1-96-en.html}, eprint = {http://maco.lu.ac.ir/article-1-96-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Parvinianzadeh, Rohollah and Pazhman, Jumakh}, title = {A Collection of Local Spectra Preserving Maps}, abstract ={We collection some results about maps on the algebra of all bounded operators that preserve the local spectrum and local spectral radius at nonzero vectors. Also, we described maps that preserve operators of local spectral radius zero at points and discuss several problems in this direction. Finally, we collection maps that preserve the local spectral subspace of operators associated with any singleton.  }, Keywords = {Local spectrum, Local spectral radius, Local spectral subspace, Nonlinear preservers, Matrices.}, volume = {3}, Number = {1}, pages = {49-60}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.6}, url = {http://maco.lu.ac.ir/article-1-104-en.html}, eprint = {http://maco.lu.ac.ir/article-1-104-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {JabbariNooghabi, Mehdi and Soori, Ali and Nasiri, Parviz and Hormozinejad, Farshin and Ghalani, Mohammadrez}, title = {Objective Bayesian Analysis For a Two-parameters Exponential Distribution}, abstract ={In any Bayesian inference problem, the posterior distribution is a product of the likelihood and the prior: thus, it is a ected by both in cases where one possesses little or no information about the target parameters in advance. In the case of an objective Bayesian analysis, the resulting posterior should be expected to be universally agreed upon by ev- eryone, whereas . subjective Bayesianism would argue that probability corresponds to the degree of personal belief. In this paper, we consider Bayesian estimation of two-parameter exponential distribution using the Bayes approach needs a prior distribution for parame- ters. However, it is dicult to use the joint prior distributions. Sometimes, by using linear transformation of reliability function of two-parameter exponential distribution in order to get simple linear regression model to estimation of parameters. Here, we propose to make Bayesian inferences for the parameters using non-informative priors, namely the (depen- dent and independent) Je reys' prior and the reference prior. The Bayesian estimation was assessed using the Monte Carlo method. The criteria mean square error was determined evaluate the possible impact of prior speci cation on estimation. Finally, an application on a real dataset illustrated the developed procedures.}, Keywords = {Jeffreys' prior, two-parameters exponential distribution, objective Bayesian analysis, posterior distribution, MSE}, volume = {3}, Number = {1}, pages = {61-71}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.7}, url = {http://maco.lu.ac.ir/article-1-103-en.html}, eprint = {http://maco.lu.ac.ir/article-1-103-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Ghaneai, Hossein and Mirabi, Mohammad and Rashidi, Rez}, title = {Numerical Investigation of Wave Equations in Large Domains via a Novel Variational Iteration Method}, abstract ={The value of an auxiliary parameter incorporated into the well-known variational iteration method (VIM) to obtain solutions of wave equations in unbounded domains is discussed in this article. The suggested method, namely the optimal variational iteration method, is investigated for convergence. Furthermore, the proposed method is tested on one-dimensional and two-dimensional wave equations in unbounded domains in order to better understand the solution mechanism and choose the best auxiliary parameter.Comparisons with results from the standard variational iteration procedure demonstrate that the auxiliary parameter is very useful in tracking the convergence field of the approximate solution.}, Keywords = {Wave equations, Unbounded domaines, Variational iteration method, Optimal variational iteration method, Auxiliary parameter, Hermite-Gauss quadrature.}, volume = {3}, Number = {1}, pages = {73-83}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.8}, url = {http://maco.lu.ac.ir/article-1-105-en.html}, eprint = {http://maco.lu.ac.ir/article-1-105-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Nazari, Alimohammad and Sherafat, Fahimeh}, title = {Construction of Nonnegative Matrix for Special Spectrum}, abstract ={The construction of a nonnegative matrix for a given set of eigenvalues is one of the objectives of this paper. The generalization of the cases discussed in the previous papers as well as finding a recursive solution for the Suleimanova spectrum are other points that are studied in this paper.}, Keywords = {‎Nonnegative matrix‎, ‎Spectrum of matrix‎, ‎Perron‎}, volume = {3}, Number = {1}, pages = {85-95}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.9}, url = {http://maco.lu.ac.ir/article-1-97-en.html}, eprint = {http://maco.lu.ac.ir/article-1-97-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {BagheriSalec, Alirez}, title = {Convolution Weighted Orlicz Algebras in Context of σ-Compact Groups}, abstract ={In this paper, the conditions are considered that a weighted Orlicz space, LΦw(G), is a Banach algebra with convolution as  multiplication in context of a locally compact σ-compact groups. We also for a class of Orlicz spaces, obtain an equivalent condition, such that a weighted Orlicz space to be a convolution Banach algebra. This resultes generalized some known results in Lebesgue spaces.}, Keywords = {locally compact group, σ-compact group, convolution algebra, weighted Orlicz space, Orlicz spaces}, volume = {3}, Number = {1}, pages = {97-103}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.10}, url = {http://maco.lu.ac.ir/article-1-107-en.html}, eprint = {http://maco.lu.ac.ir/article-1-107-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {MaysamiSadr, Maysam}, title = {A Note on The Best Approximation in Spaces of Affine Functions}, abstract ={The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some linear versions of an old result due to Mazur. For the proofs we use some sandwich theorems of Fenchel's duality theory.  }, Keywords = {Best approximation, convex set, affine function, sandwich theorem.}, volume = {3}, Number = {1}, pages = {105-107}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.11}, url = {http://maco.lu.ac.ir/article-1-106-en.html}, eprint = {http://maco.lu.ac.ir/article-1-106-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Dadsetadi, Somayyeh and Torkzadeh, Leila and Nouri, Kazem}, title = {Existence and uniqueness solution of the Hammerstein type fractional equations via the fixed point theorems}, abstract ={The aim of this paper is to investigate the existence and uniqueness of solution for a class of nonlinear integro-differential equations known as Hammerstein type. We study fractional equations in the Banach space whose derivative is of the Caputo type. The existence of solution is studied by using the Schauder's fixed point theorem, and the uniqueness is established via a generalization of the Banach fixed point theorem. Finally, an example is given to illustrate the analytical findings.}, Keywords = {Fractional Hammerstein integro-differential equations, Existence and uniqueness, Schauder's fixed point theorem, Banach fixed point theorem.}, volume = {3}, Number = {1}, pages = {109-115}, publisher = {Lorestan University}, doi = {10.52547/maco.3.1.12}, url = {http://maco.lu.ac.ir/article-1-110-en.html}, eprint = {http://maco.lu.ac.ir/article-1-110-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {mazaheri, H. and Jesmani, S.M}, title = {Equivalence Relations On Best Co-Approximation and Worst Co-Aapproximation}, abstract ={A kind of approximation, called best coapproximation was introduced and discussed in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by several researchers in different abstract spaces. In this paper, we define relations on best coapproximation and worst coapproximation. We show that these relations are equivalence relation. We obtain cosets sets of best coapproximation and worst approximation. We obtain some results on these sets, compactness and weakly compactness and define coqproximinal and coqremotal.}, Keywords = {Cochebyshev sets, Cosets best coaprrpximation sets, Cosets worst coapproximation, Coqproximinal, Coqremotal, Equivalence relations}, volume = {3}, Number = {2}, pages = {119-127}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.11}, url = {http://maco.lu.ac.ir/article-1-117-en.html}, eprint = {http://maco.lu.ac.ir/article-1-117-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Taheri, Hossein and Eghbali, Nasrin and Pourabd, Masoumeh and Zhu, Huaiping}, title = {Assessment of the Mathematical Model for Investigating Covid-19 Peak as A Global Epidemic in Iran}, abstract ={In this paper, we investigate the COVID-19 pandemic in Iran from a mathematical modeling perspective. By improving the well-known susceptible infected recovered (SIR) family of compartmental models and adding unreported cases obtain a local model for Iran. Since we only want infected cases, we have refused to add other classes which there are can be. we estimate the infected case by using the reported data of the first period of the outbreak and will apply the results to data of the provinces of Ardabil and Guilan which were available to us as well as published data from Iran. We show that, if some of the indexes are constant, the future infectious reported cases are predictable. Also, we show a good agreement between the reported data and the estimations given by the proposed model. We further demonstrate the importance of choosing this proposed model used to by finding the basic reproductive number. Also, we will estimate the probability distribution for the death rate. Our study can help the decision-making of public health.}, Keywords = {Corona-virus pandemic globally, Mathematical modeling, SIRU-model, Parameter identification, Statistical methods, Akaike information criterion.}, volume = {3}, Number = {2}, pages = {129-142}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.12}, url = {http://maco.lu.ac.ir/article-1-127-en.html}, eprint = {http://maco.lu.ac.ir/article-1-127-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {IloonKashkooly, Ali and Baseri, Gholamreza and Rezaei, Hami}, title = {On Subspace Balanced Convex-Cyclic Operators}, abstract ={Abstract. Let X be a separable Banach space and M be a subspace of X. A bounded Linear operator T on X is subspace balanced convex-cyclic for a subspace M, if there exists a vector x∈X such that the intersection of balanced convex hull of orb(T,x) with M is dense in M. We give an example of subspace balanced convex-cyclic operator that is not balanced convex-cyclic. Also we give an improvement of the Kitailike criterion for subspace balanced convex-cyclicity and bring on with the Hahn-Banach characterization for subspace balanced convex-cyclicity.}, Keywords = {Balanced convex-cyclic operators, Kitai criterion, Hahn Banach theorem}, volume = {3}, Number = {2}, pages = {1-6}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.1}, url = {http://maco.lu.ac.ir/article-1-111-en.html}, eprint = {http://maco.lu.ac.ir/article-1-111-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Rashedi, Kamal}, title = {Detection of a time-dependent forcing term in a one-dimensional wave equation with a dynamic-type boundary condition}, abstract ={In the current paper, we study an inverse problem of identifying a time-dependent forcing term in the one-dimensional wave equation. We have the information of the wave displacement at two different instants of time and two sensor locations of space along with a dynamic type boundary condition. We prove the unique solvibility of the problem under some regularity and consistency conditions. Then, an approximate solution of the given inverse problem based upon deploying the Ritz technique along with the the collocation method is presented which converts the problem to a linear system of algebraic equations. The method takes advantage of the Tikhonov regularization technique to solve the linear system of equations that is not well-conditioned in order to achieve stable solutions. Numerical findings are also included to support the claim that the presented method is reliable in finding accurate and stable solutions.  }, Keywords = {Inverse source problems, dynamic-type boundary condition, collocation method, Tikhonov Regularization}, volume = {3}, Number = {2}, pages = {7-16}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.2}, url = {http://maco.lu.ac.ir/article-1-114-en.html}, eprint = {http://maco.lu.ac.ir/article-1-114-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Taghavi, Ali}, title = {Topological and Banach Space interpretation for real sequences whose consecutive terms have a bounded difference}, abstract ={ In this paper we give a topology-dynamical interpretation for the space  of all integer sequences $P_n$ whose consecutive difference $P_{n+1}-P_n$ is a bounded sequence.  We also introduce a new concept textit{"Rigid Banach space"}. A rigid  Banach space is a Banach space $X$  such that for  every continuous linear injection $j:Xto X,;overline{J(X)}$ is either isomorphic to $X$ or it does not contain any isometric copy of $X$. We prove that $ell_{infty}$ is not a rigid Banach space. We also  discuss about  rigidity of Banach algebras.}, Keywords = {Rigid Banach space, sequence space, Primes}, volume = {3}, Number = {2}, pages = {17-24}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.3}, url = {http://maco.lu.ac.ir/article-1-113-en.html}, eprint = {http://maco.lu.ac.ir/article-1-113-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Tayebi, Akbar and Eslami, Faezeh}, title = {On Conformal Transformation of Some Non-Riemannian Curvatures in Finsler Geometry}, abstract ={In this paper, we study the conformal transformation of some important and effective non-Riemannian curvatures in Finsler Geometry.   We find the necessary and sufficient condition under which the conformal transformation preserves the  Berwald curvature  B, mean Berwald curvature  E, Landsberg curvature  L, mean Landsberg curvature  J, and the non-Riemannian curvature  H.}, Keywords = {Berwald curvature, mean Berwald curvature, Landsberg curvature, mean Landsberg curvature, the quantity H.}, volume = {3}, Number = {2}, pages = {25-34}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.4}, url = {http://maco.lu.ac.ir/article-1-118-en.html}, eprint = {http://maco.lu.ac.ir/article-1-118-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {KhaleghiMoghadam, Mohse}, title = {A survey on multiplicity results for fractional difference equations and variational method}, abstract ={In this paper, we deal with the existence and multiplicity solutions, for the following fractional  discrete boundary-value problem begin{equation*} begin{cases} _{T+1}nabla_k^{alpha}left( ^{}_knabla_{0}^{alpha}(u(k))right)+{^{}_knabla}_{0}^{alpha}left( ^{}_{T+1}nabla_k^{alpha}(u(k))right)=lambda f(k,u(k)), quad k in [1,T]_{mathbb{N}_{0}}, u(0)= u(T+1)=0, end{cases} end{equation*} where $0leq alphaleq1$ and $^{}_{0}nabla_k^{alpha}$ is  the left nabla discrete fractional difference  and $^{}_knabla_{T+1}^{alpha}$ is the right nabla discrete fractional difference  and   $f: [1,T]_{mathbb{N}_{0}}timesmathbb{R}tomathbb{R}$ is a continuous function and $lambda>0$ is a parameter. The technical approach is based on the critical point theory and some local minimum theorems for differentiable functionals. Several examples are included to illustrate the main results. textbf{MSC(2010):} 26A33; 39A10; 39A27. textbf{Keywords:}  Discrete fractional calculus, Discrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory. }, Keywords = {Discrete fractional calculus, Discrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory.}, volume = {3}, Number = {2}, pages = {35-58}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.5}, url = {http://maco.lu.ac.ir/article-1-108-en.html}, eprint = {http://maco.lu.ac.ir/article-1-108-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Malekinejad, Somayeh}, title = {New Inequalities Involving Operator Means for Sector Matrices}, abstract ={The main goal of this paper is to discuss the Callebaut inequality and mean-convex inequality from positive definite matrices to sector matrices in a more general setting. Afterward, several inequalities involved positive linear map, are presented for sector matrices. For instance, we show that if $ A,Bin {{mathcal S}_{alpha}}$ are two sector matrices, then for all $sigmageqsharp$ we have begin{equation*} mathcal{R}(Phi^{-1}left( A sigma B)right)leq sec^2alpha~mathcal{R} (Phi(A^{-1})sharp Phi(B^{-1})).}, Keywords = {Callebaut inequality, Positive linear map, Sector matrices, Semi-self-adjoint mean.}, volume = {3}, Number = {2}, pages = {59-67}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.6}, url = {http://maco.lu.ac.ir/article-1-119-en.html}, eprint = {http://maco.lu.ac.ir/article-1-119-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Banimehri, Saeed and Esmaeili, Hami}, title = {A new modified line search algorithm to solve large-scale non-smooth non-convex optimization problem}, abstract ={‎In this paper‎, ‎a new modified line search Armijo is used in the diagonal discrete gradient bundle method to solve large-scale non-smooth optimization problems‎. ‎The new principle causes the step in each iteration to be longer‎, ‎which reduces the number of iterations‎, ‎evaluations‎, ‎and the computational time‎. ‎In other words‎, ‎the efficiency and performance of the method are improved‎. ‎We prove that the diagonal discrete gradient bundle method converges with the proposed monotone line search principle for semi-smooth functions‎, ‎which are not necessarily differentiable or convex‎. ‎In addition‎, ‎the numerical results confirm the efficiency of the proposed correction‎.}, Keywords = {Non-smooth optimization‎, ‎Derivative-free optimization‎, ‎Diagonal discrete gradient bundle method‎, ‎line search}, volume = {3}, Number = {2}, pages = {69-76}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.7}, url = {http://maco.lu.ac.ir/article-1-121-en.html}, eprint = {http://maco.lu.ac.ir/article-1-121-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Ogbereyivwe, Oghovese and Umar, Shehu Salisu}, title = {Modified Householder Iterative Scheme requiring no Function Derivative for Solving Nonlinear Equations.}, abstract ={The Householder iterative scheme (HIS) for determining solution of equations that are nonlinear have existed for over fifty decades and have enjoyed several modifications in literature. However, in most HIS modifications, they usually require function derivative evaluation in their implementation. Obtaining derivative of some functions is difficult and in some cases, it is not achievable.To circumvent this setback, the divided difference operator was utilised to approximate function derivatives that appear in the scheme. This resulted to the development of a new variant of the HIS with high precision and require no function derivative. The theoretical convergence of the new scheme was established using Taylor’s expansion approach. From the computational results obtained when the new scheme was tested on some non-linear problems in literature, it performed better than the Householder scheme.  }, Keywords = {Nonlinear equation, Iterative scheme, Householder iterative scheme, Derivative free.}, volume = {3}, Number = {2}, pages = {77-82}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.8}, url = {http://maco.lu.ac.ir/article-1-124-en.html}, eprint = {http://maco.lu.ac.ir/article-1-124-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Abolghasemi, Mohammad and Moradi, Shahi}, title = {Existence of three classical solutions for impulsive fractional boundary value problem with $p$-Laplacian}, abstract ={In this paper, we study the existence of at least three distinct solutions for a class of impulsive fractional boundary value problems with $p$-Laplacian with Dirichlet boundary conditions. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces. One example is presented to demonstrate the application of our main results.}, Keywords = {Fractional $p$-Laplacian, Impulsive effects, Three solutions, Variational methods}, volume = {3}, Number = {2}, pages = {83-103}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.9}, url = {http://maco.lu.ac.ir/article-1-125-en.html}, eprint = {http://maco.lu.ac.ir/article-1-125-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} } @article{ author = {Lotfi, Mahmou}, title = {Legendre spectral element and backward Euler methods for solving a family of stochastic partial differential equations}, abstract ={In this paper, we use the spectral element method for solving the stochastic partial differential equation. For spatial discretization, we use the Legendre spectral element method, and we obtain the semi-discrete form. To solve the problem, we need to obtain the complete discrete form and we use the backward Euler method to this aim. The Weiner process is approximated by Fourier series and we obtain the fully discrete scheme of the problem. Error and convergence analysis are presented and, with a numerical example, we demonstrate the efficiency of the proposed method.}, Keywords = {Stochastic partial differential equation, spectral element method, Legendre polynomials}, volume = {3}, Number = {2}, pages = {105-118}, publisher = {Lorestan University}, doi = {10.22034/maco.3.2.10}, url = {http://maco.lu.ac.ir/article-1-122-en.html}, eprint = {http://maco.lu.ac.ir/article-1-122-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2022} }