STRONG CONVERGENCE THEOREMS BY THE HYBRID METHOD FOR FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES

Abstract

Let $C$ be a nonempty closed convex subset of a real Hilbert space and let $\{T_n\}$ be a family of mappings of $C$ into itself such that the set of all common fixed points of $\{T_n\}$ is nonempty. We consider a sequence $\{x_n\}$ generated by the hybrid method in mathematical programming and give the conditions of $\{T_n\}$ under which $\{x_n\}$ converges strongly to a common fixed point of $\{T_n\}$.