Hybrid Projection Algorithm for Generalized Split Equilibrium Problem in Hibert Spaces

Abstract

In this thesis we suggest and examine Extra Gradient-Proximal Point algorithm to find the solution of Split Equilibrium Problem and Fixed Point Problem for nonexpansive semigroup in real Hilbert spaces. Our purpose is to address fixed point problems(FPP), variational inequality problems (VIP) and generalized Split Equilibrium Problems(GSEP) in the setting of Hilbert spaces. We propose a hybrid shrinking projection algorithm, which exhibits strong convergence, for the construction of a common element in the set of common fixed points of an infinite family of k-strict pseudo-contractions and the set of common solutions of a finite family of Generalized Split Equilibrium Problems(GSEP) in Hilbert spaces. Our results generalize and improve various existing results in the current literature.