Strong convergence theorems for an infinite family of quasi-nonexpansive mappings and generalized equilibrium problems and variational inequality problems

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of an infinite family of uniformly continuous quasi-nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element of the three mentioned sets. Our results extend important recent results.     

New strong convergence method for the sum of two maximal monotone operators

Optimization and Engineering - This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of...     

Nonlinear iterative methods for solving the split common null point problem in Banach spaces

In this work, we study the split common null point problem in the framework of Banach spaces. We propose an iterative scheme for solving the problem and then prove strong convergence theorem of the sequences generated by our iterative scheme under suitable conditions. We finally provide some numerical examples to support the main theorem.     

Extragradient Algorithm for Solving Pseudomonotone Equilibrium Problem with Bregman Distance in Reflexive Banach Spaces

Networks and Spatial Economics - Using the Bregman distance technique, we study the approximation of solution of pseudomonotone equilibrium problem using modified extragradient method in a real...     

A strong convergence theorem for a general split equality problem with applications to optimization and equilibrium problem

The purpose of this paper is to introduce and study an iterative algorithm for solving a general split equality problem. The problem consists of finding a common element of the set of common zero points for a finite family of maximal monotone operators, the set of common fixed points for a finite family of demimetric mappings and the set of common solutions of variational inequality problems for a finite family of inverse strongly monotone mappings in the setting of infinite-dimensional Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating a solution of the split equality problem. As special cases, we shall utilize our results to study the split equality equilibrium problems and the split equality optimization problems. Our result complements and extends some related results in literature.     

An alternated inertial method for pseudomonotone variational inequalities in Hilbert spaces

Optimization and Engineering - In this paper, we introduce a new relaxed extrgadient algorithm with alternated inertial extrapolation step and self adaptive variable stepsizes for solving...