A New Hybrid Iterative Algorithm for Fixed-Point Problems, Variational Inequality Problems, and Mixed Equilibrium Problems

A New Hybrid Iterative Algorithm for Fixed-Point Problems, Variational Inequality Problems, and Mixed Equilibrium Problems

We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium problem. This study, proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point ...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Modified hybrid iterative methods for generalized mixed equilibrium, variational inequality and fixed point problems

In this paper, we introduce two modified hybrid iterative methods (one implicit method and one explicit method) for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality problem for a continuous monotone mapping and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces, and show...

A Hybrid Iterative Scheme for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Banach Spaces

The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-stronglymonotone operator and the set of fixed points of relatively quasinonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtai...

On variational inequality, fixed point and generalized mixed equilibrium problems

*Correspondence: [email protected] 1School of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China Full list of author information is available at the end of the article Abstract In this article, variational inequality, fixed point, and generalized mixed equilibrium problems are investigated based on an extragradient iterative algor...