Solving Equilibrium Problem and Fixed Point Problem by Normal S-iteration Process in Hilbert Space

Abstract

The main purpose of this paper is to find a common element in the solution set of equilibrium problem and fixed point problem of non-expansive mappings in the real Hilbert space with the help of normal S-iteration process. Also, under some acceptable assumptions, we prove the sequences induced by above stated process converge weakly to a point in the solution set of above stated problems. At the end, we give a numerical example to justify our work. The results studied in this work philosophize and boost some contemporary and known results in this direction.

Keywords

• equilibrium problem
• normal s-iteration
• ; fixed point problem
• ; hilbert space
• non-expansive mapping