Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Equivalence Relations On Best Co-Approximation and Worst Co-Aapproximation
119
127
EN
H.
mazaheri
Yazd University
S.M
Jesmani
Department of Materials and Metallurgical Engineering, Technical and Vocational University(TVU), Tehran, Iran
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Assessment of the Mathematical Model for Investigating Covid-19 Peak as A Global Epidemic in Iran
129
142
EN
Hossein
Taheri
University of Mohaghegh Ardabili
Nasrin
Eghbali
University of Mohaghegh Ardabili
Masoumeh
Pourabd
University of Mazandaran
Huaiping
Zhu
York University
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
On Subspace Balanced Convex-Cyclic Operators
1
6
EN
Ali
Iloon Kashkooly
Yasouj University
Gholamreza
Baseri
Yasouj University
Hamid
Rezaei
Yasouj University
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Detection of a time-dependent forcing term in a one-dimensional wave equation with a
dynamic-type boundary condition
7
16
EN
Kamal
Rashedi
University of Science and Technology of Mazandaran
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Topological and Banach Space interpretation for real sequences whose consecutive terms have a bounded difference
17
24
EN
Ali
Taghavi
Qom University of technology
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
On Conformal Transformation of Some Non-Riemannian Curvatures in Finsler Geometry
25
34
EN
Akbar
Tayebi
University of Qom
Faezeh
Eslami
University of Qom
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
A survey on multiplicity results for fractional difference equations and variational method
35
58
EN
Mohsen
Khaleghi Moghadam
Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
New Inequalities Involving Operator Means for Sector Matrices
59
67
EN
Somayeh
Malekinejad
Payame Noor University
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})).
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
A new modified line search algorithm to solve large-scale non-smooth non-convex optimization problem
69
76
EN
Saeed
Banimehri
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.
Hamid
Esmaeili
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Modified Householder Iterative Scheme requiring no Function Derivative for Solving Nonlinear Equations.
77
82
EN
Oghovese
Ogbereyivwe
Delta State Univ. of Sc. and Tech., Ozoro, Nigeria.
Shehu Salisu
Umar
Auchi Polytechnic, Auchi
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Existence of three classical solutions for impulsive fractional boundary value problem with $p$-Laplacian
83
103
EN
Mohammad
Abolghasemi
Razi University
Shahin
Moradi
Razi University
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.
Lorestan University
Mathematical Analysis and Convex Optimization
2717-0624
3
2
2022
12
1
Legendre spectral element and backward Euler methods for solving a family of stochastic partial differential equations
105
118
EN
Mahmoud
Lotfi
Farhangian University
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.