# Convergence Theorems for Modified Mann Reich-Sabach Iteration Scheme for Approximating the Common Solution of Equilibrium Problems and Fixed Point Problems in Hilbert Spaces with Numerical Examples

## Keywords:

Hilbert spaces, k-strictly pseudocontractive-type mapping, strong convergence, strict fixed point sets, equilibrium problem, finite families## Abstract

**Communication in Physical Sciences 2020, 5(4): 482-496**

**Received ****25 May 2017****/Revised 9 ****May 2018**/**Accepted 20 February 2020**

It is proved that the modified Reich-Sabach iteration scheme introduced recently by Isiogugu et al. in a real Hilbert space , converges strongly to a common element of the fixed point sets of a finite family of multi-valued strictly pseudocontractive-type mappings and the set of solutions of a finite family of equilibrium problems. This work is a continuation of the study on the computability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of the sequences and , from an arbitrary , where , , while is the projection map and is the sequence of the resolvent of the bifunction. The obtained results improve, complement and extend many results on equilibrium problems, multi-valued and single-valued mappings in the contemporary literature.

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