Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities, By Hossein Piri

Research

Title	Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities
Type	Article
Keywords	projection, common fixed point, amenable semigroup, iterative process, strong convergence, variational inequality
Researchers	Hossein Piri، Ali Haji-Badali

Abstract

In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for b-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common element of the above two sets.