Approximation Method for Fixed Point Problem and Variational Inequality Problem without Assumption on the Set of Fixed Pint and the Set of Variational Inequality

Atid Kangtunyakarn

Abstract

The purpose of this paper is to prove a necessary and sufficient condition to obtain strong convergence theorem for finding a common element of the set of fixed point problem of nonexpansive mapping and the set of variational inequality problem without assumption $F(T)\bigcap VI(C,A)\neq\emptyset$ in framework of Hilbert space.