@article{ author = {Khatibzadeh, Hadi and Rezaei, Mahnaz}, title = {On the Existence of Solutions of a Generalized Monotone Equilibrium Problem}, abstract ={Blum and Oettli in their seminal paper studied monotone bifunctions and proved the existence of an equilibrium point. In this work, we extend theirmain result by replacing monotone bifunction with a more general bifunction and prove the existence of an equilibrium point.}, Keywords = {Equilibrium problem, Monotone bifunction, Generalized monotonicity, Equilibrium point}, volume = {1}, Number = {1}, pages = {1-5}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.1}, url = {http://maco.lu.ac.ir/article-1-22-en.html}, eprint = {http://maco.lu.ac.ir/article-1-22-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Pirhadi, Vahi}, title = {A `xi`-Projectively Flat Connection on Kenmotsu Manifolds}, abstract ={‎In this paper‎, ‎we introduce a semi-symmetric non-metric connection on `eta`-Kenmotsu manifolds that changes an `eta`-Kenmotsu manifold into an Einstein manifold‎. ‎Next‎, ‎we consider an especial version of this connection and show that every Kenmotsu manifold is `xi`-projectively flat with respect to this connection‎. ‎Also‎, ‎we prove that if the Kenmotsu manifold `M` is a `xi`-concircular flat with respect to the new connection‎, ‎then `M` is necessarily of zero scalar curvature‎. ‎Then‎, ‎we review the sense of `xi`-conformally flat on Kenmotsu manifolds and show that a `xi`-conformally flat Kenmotsu manifold with respect to the new connection is an `eta`-Einstein with respect to the Levi-Civita connection‎. ‎Finally‎, ‎we prove that there is no `xi`-conharmonically flat Kenmotsu manifold with respect to this connection‎.}, Keywords = {‎Kenmotsu manifold‎, ‎`eta`-Einstein manifold‎, ‎`xi`-concircular flat manifold‎, `xi`-conformally flat manifold‎, ‎`xi`-conharmonically flat manifold‎, ‎`xi`-projectively flat manifold‎.}, volume = {1}, Number = {1}, pages = {7-14}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.2}, url = {http://maco.lu.ac.ir/article-1-39-en.html}, eprint = {http://maco.lu.ac.ir/article-1-39-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Safaei, Nozar and Barani, Ali}, title = {Schur-Convexity of Integral Arithmetic Means of Co-Ordinated Convex Functions in `R^3`}, abstract ={In this paper, we investigate Schur-convexity of some functions which are obtained from the co-ordinated convex functions on a rectangular box in `R^3`.}, Keywords = {Schur-convexity, Convex functions on the co-ordinates.}, volume = {1}, Number = {1}, pages = {15-24}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.3}, url = {http://maco.lu.ac.ir/article-1-35-en.html}, eprint = {http://maco.lu.ac.ir/article-1-35-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Nyamoradi, Neamat and Teng, Kaimi}, title = {Existence of Three Solutions for Hemi-variational Inequalities Driven With Impulsive Effects}, abstract ={In this paper we prove the existence of at least three solutions to the following second-order impulsive system:   where `A: [0, T] rightarrow mathbb{R}^{N times N}` is a continuous map from the interval `[0, T]` to the set of `N`-order symmetric matrixes. The approach is fully based on a recent three critical points theorem of Teng [K. Teng, Two nontrivial solutions for hemivariational inequalities driven by nonlocal elliptic operators, Nonlinear Anal. (RWA) 14 (2013) 867-874].}, Keywords = {Nonsmooth critical point, Variational methods, Locally Lipschitz, Impulsive.}, volume = {1}, Number = {1}, pages = {25-39}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.4}, url = {http://maco.lu.ac.ir/article-1-41-en.html}, eprint = {http://maco.lu.ac.ir/article-1-41-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Abbasi, Naser and Moiseev, Evgenii Ivanovich}, title = {On the Basis Property of an Trigonometric Functions System of The Frankl Problem With a Non-Local Parity Condition of the First Kind in the Sobolev Space `overline(W)_p^(2l) (0,pi)`}, abstract ={In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal parity condition of the first kind. We analyze the  completeness,  the basis  property,  and the minimality of the eigenfunctions  in the space `overline(W)_p^(2l) (0,pi)`,  where  `overline(W)_p^(2l) (0,pi)` be the set of functions `f in  W_p^(2l) (0,pi)`, satisfying of the following conditions: `f^{(2k-1)}(0)=0, k=1,2,...,l`.}, Keywords = {Frankl problem, Lebesgue integral, Holder inequality, Bessel equation, Sobolev space}, volume = {1}, Number = {1}, pages = {41-48}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.5}, url = {http://maco.lu.ac.ir/article-1-43-en.html}, eprint = {http://maco.lu.ac.ir/article-1-43-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Rahimi, Mehdi and Assari, Amir}, title = {Mutual Entropy Map for Continuous Systems on Compact Metric Spaces}, abstract ={In this paper we introduce the concept of mutual entropy map for continuous maps on metric spaces. It is a non-negative extended real number which depends on two measures which are preserved by a system. Then we will extract the Kolmogorov entropy of ergodic systems from the mutual entropy as a special case when the two measures are equal.}, Keywords = {Entropy, Invariant, Mutual entropy.}, volume = {1}, Number = {1}, pages = {49-55}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.6}, url = {http://maco.lu.ac.ir/article-1-42-en.html}, eprint = {http://maco.lu.ac.ir/article-1-42-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Aleomraninejad, Seyyed Mohamad Ali and Solaimani, Mehdi}, title = {Numerical Solution of Some Non-Linear Eigenvalue Differential Equations by Finite Difference-Self Consistent Field Method}, abstract ={The finite difference-self consistent field iteration is presented to solve some non-linear eigenvalue differential equations‎.Some properties of the self consistent field iteration and finite difference methods required for our subsequent development are given‎. ‎Numerical examples are included to demonstrate the validity and applicability of the present technique. A comparison is also made with the existing results‎. ‎The method is easy to implement and yields accurate results‎.‎‎}, Keywords = {Non-linear eigenvalue differential equation, Finite difference method, Self consistent field iteration}, volume = {1}, Number = {1}, pages = {57-64}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.7}, url = {http://maco.lu.ac.ir/article-1-40-en.html}, eprint = {http://maco.lu.ac.ir/article-1-40-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Ranjbar, Mojtaba and Pourghanbar, Somayeh and Nasrabadi, Ebrahim}, title = {An Analytical Solution for the Black-Scholes Equation Using Functional Perturbation Method}, abstract ={One of the greatest accomplishments in modern financial theory, in terms of both approach and applicability has been the BlackScholes option pricing model. It is widely recognized that the value of a European option can be obtained by solving the Black-Scholes equation. In this paper we use functional perturbation method (FPM) for solving Black-Scholes equation to price a European call option. The FPM is a tool based on considering the differential operator as a functional. The equation is expanded functionally by Frechet series. Then a number of successive partial differential equations (PDEs) are obtained that have constant coefficients and differ only in their right hand side part. Therefore we do not need to resolve the different equations for each step. In contrast to methods that have implicit solutions, the FPM yields a closed form explicit solution.}, Keywords = {Black-Scholes equation, European call option, Functional perturbation method}, volume = {1}, Number = {1}, pages = {65-74}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.8}, url = {http://maco.lu.ac.ir/article-1-44-en.html}, eprint = {http://maco.lu.ac.ir/article-1-44-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Thierno, Sow}, title = {General Viscosity Iterative Process for Solving Variational Inclusion and Fixed Point Problems Involving Multi-Valued Quasi-Non-Expansive and Demicontractive Operators With Application}, abstract ={In this paper, we  introduce and study a new iterative method which is based on viscosity general algorithm and forward-backward splitting method  for finding a common element of the set of common fixed points of multivalued demicontractive and quasi-nonexpansive mappings and the set of solutions of  variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings in  real Hilbert spaces. We prove that the sequence $x_n$ which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, our theorems are applied to approximate a common solution of fixed point problems with set-valued operators and the composite convex minimization problem. Our theorems are significant improvements on several important recent results.}, Keywords = {Common fixed points, Variational inclusion problems, Set-valued operators, Iterative methods}, volume = {1}, Number = {1}, pages = {75-91}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.10}, url = {http://maco.lu.ac.ir/article-1-37-en.html}, eprint = {http://maco.lu.ac.ir/article-1-37-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {AnaloueiAdegani, Ebrahim and Bota, Monica-Felici}, title = {Coupled Coincidence Point Results for Mappings Without Mixed Monotone Property in Partially Ordered `G`-Metric Spaces}, abstract ={In this paper, we prove some coupled fixed point theorems for nonlinear contractive mappings which doesn't have the mixed monotone property, in the context of partially ordered `G`-metric spaces. Hence, these results can be applied in a much wider class of problems. Our results improve the result of D. Dori'{c}, Z. Kadelburg and S. Radenovi'{c} [Appl. Math. Lett. (2012)]. We also present two examples to support these new results.}, Keywords = {`G`-metric space, coupled common fixed point, mixed monotone property}, volume = {1}, Number = {1}, pages = {93-106}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.9}, url = {http://maco.lu.ac.ir/article-1-46-en.html}, eprint = {http://maco.lu.ac.ir/article-1-46-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {ThiHongDiem, Huynh}, title = {Variational Approximations of a Dual Pair of Mathematical Programming Problems}, abstract ={We study variational approximations of a dual pair of mathematical programming problems in terms of epi/hypo-convergence and inside epi/hypo-convergence of approximating Lagrange functions of the pair. First, the Painlevé -Kuratowski convergence of approximate saddle points of approximating Lagrange functions is established under the inside epi/hypo-convergence of these approximating Lagrange functions. From this, we obtain a couple of solutions of the pair of problems and a strong duality. Under a stronger variational convergence called ancillary tight epi/hypo-convergence, we obtain the Painle vé-Kuratowski convergence of approximate minsup-points and approximate maxinf-points of approximating Lagrange functions (when approximate saddle points are not necessary to exist).}, Keywords = {Variational approximations, mathematical programming, epi/hypo-convergence, inside epi/hypo-convergence, ancillary tightness, Lagrange functions, strong duality, approximate saddle points, approximate minsup-points, approximate maxinf-points}, volume = {1}, Number = {1}, pages = {107-118}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.11}, url = {http://maco.lu.ac.ir/article-1-49-en.html}, eprint = {http://maco.lu.ac.ir/article-1-49-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} } @article{ author = {Jafari, Somaye}, title = {Optimality Conditions for Solving Nonconvex Set-Valued Equilibrium Problems}, abstract ={In this paper, sufficient conditions ensuring the existence of solutions for set-valued equilibrium problems are obtained. The convexity assumption on the whole domain is not necessary and just the closure of a quasi-self-segment-dense subset of the domain is convex. Using a KKM theorem and a notion of Q-selected preserving $R_{-}^{*}$-intersection ($R_{-}^{*}$-inclusion) for set-valued mapping, the existence results are proved in real Hausdorff topological vector spaces.}, Keywords = {Set-valued equilibrium problem, Quasi-self-segment-dense set, Quasiconvexity, Generalized semicontinuity, Topological vector space.}, volume = {1}, Number = {1}, pages = {119-128}, publisher = {Lorestan University}, doi = {10.29252/maco.1.1.12}, url = {http://maco.lu.ac.ir/article-1-48-en.html}, eprint = {http://maco.lu.ac.ir/article-1-48-en.pdf}, journal = {Mathematical Analysis and Convex Optimization}, issn = {2717-0624}, eissn = {2717-0624}, year = {2020} }