HYBRID METHOD FOR A FAMILY OF MAPPINGS WITH APPLICATIONS IN ZERO OF MAXIMAL MONOTONE OPERATORS

Abstract

In this paper, we construct some algorithms for finding common fixed point of a
family of mappings with some sfficient condition. In fact, let C be a nonempty closed convex
subset of a uniformly convex Banach space X whose norm is Gateaux differentiable and let
{T_n} be a family of self-mappings on C such that the set of all common fixed points of {T_n} is
nonempty. We construct a sequence {x_n} generated by the hybrid method in mathematical
programming and also we give the conditions of {T_n} under which {x_n} converges strongly
to a common fixed point of {T_n}. Finally, we apply our results to zero of maximal monotone
operators.