Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators

A strong convergence theorem for solutions of zero point problems and fixed point problems

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.

Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems

We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi’s hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is pr...

Strong Convergence of an Iterative Method for Variational Inequality Problems and Fixed Point Problems

In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...