Approximation Method for Fixed Points of Nonlinear Mapping and Variational Inequalities with Application

Kanyarat Cheawchan, Atid Kangtunyakarn

Abstract

In this paper, we introduce the new method of iterative scheme $\{x_{n}\}$ for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of solutions of a modified system of variational inequalities without demiclose condition and $T_{\omega}:= (1-\omega)I+\omega T,$ when $T$ is a quasi-nonexpansive mapping and $\omega \in (0,\frac{1}{2})$ in a framework of Hilbert space. Using our main result, we obtain strong convergence theorems involving a finite family of nonspreading mapping and another corollary.