A Modified Thakur Three-Step Iterative Algorithm to Garcia-Falset Mappings and Variational Inequalities

Three-Step Methods for Nonexpansive Mappings and Mixed Variational Inequalities

In this paper, we suggest and analyze three-step iteration methods for finding the common element of the set of fixed points of nonexpansive mappings and the set of solutions of the mixed variational inequalities. We also study the convergence criteria of three-step iterative method under some mild conditions. Our results are new and interesting and include the previous results as special cases.

Iterative Methods for Semigroups of Nonexpansive Mappings and Variational Inequalities

We introduce an iterative method for finding a common fixed point of a semigroup of nonexpansive mappings in a Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real valued functions of the semigroup. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optima...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the a...

Convergence and Stability of a Three-step Iterative Algorithm for a General Quasi-variational Inequality Problem

We consider a general quasi-variational inequality problem involving nonlinear, nonconvex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasivariational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variationa...