A modified iterative method for capturing a common solution of split generalized equilibrium problem and fixed point problem

Abstract

A new iterative method is proposed based on hybrid viscosity approximation method and hybrid steepest-descent method to approximate a common solution of a split generalized equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings. We prove that the sequences generated by the iterative schemeconverges strongly to a common solution of the above said problems. Applications and numerical results are also given to illustrate the effectiveness and superiority of the proposed algorithm.