### 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.

**Published:**2014-10-03

**How to Cite this Article:**Hossein Piri, 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, J. Semigroup Theory Appl., 2014 (2014), Article ID 5 Copyright © 2014 Hossein Piri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

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