An implicit iterative process for solution system of equilibrium problems and fixed point problems of an amenable semigroup and infinite family of non-expansive mappings

Abstract

In this paper, using δ- strongly monotone and λ- strictly pseudo-contractive (in the terminology of Browder-Petryshyn type) mapping F on a real Hilbert space H, we introduce an implicit iterative scheme to find a common element of the set of solutions of a system of equilibrium problems and the set of fixed points of amenable semigroup of non-expansive mappings and infinite family of non-expansive mappings on H, with respect to a sequence of left regular means defined on an appropriate space of bounded real valued functions of semigroup. Then, we prove the convergence of sequence generated by the suggested algorithm to a unique solution of the variational inequality.