in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

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in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

Abstract. The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler–Lagrange type for the basic, isoperimetric, and Lagrange variational problems are proved, as well as transversality and sufficient optimality conditions. This allows to obtain necessary and sufficient Pareto optimality conditions for ...

In this paper, we study variational inequalities with multivalued mappings. By employing Fan's lemma, we establish the existence result for the dual formulation of variational inequalities with semistrictly quasimonotone mappings. We also show that similar results for quasimonotone variational inequalities do not hold.

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. Numerical stability and efficiency of the new method is examined through its ap...

The applicant develops new tools of variational analysis; in particular, two new versions of the Ekeland variational principle and subdifferential variational principle for set-valued mappings, as well as new constructions of extremal set systems. They play a significant role to studying an important class of constrained optimization problems called Multiobjective Optimization Problems with Equ...

Variational analysis has been recognized as a rapidly growing and fruitful area in mathematics concerning mainly the study of optimization and equilibrium problems, while also applying perturbation ideas and variational principles to a broad class of problems and situations that may be not of a variational nature. It can be viewed as a modern outgrowth of the classical calculus of variations, o...