Inertial Iterative Algorithm of Generalized f - Projection Method for Fixed point Problem, Maximal Monotone Operators and Generalized Mixed Equilibrium Problems

Abstract

The aim of this article is to investigate fixed point problem, maximal monotone operators and generalized mixed equilibrium problems by considering the generalized f− projection technique. We propose a modified inertial based algorithm for finding a common solution in respect of this problem. Also, we prove a strong convergence of the sequence generated by the proposed modified inertial iterative algorithm in uniformly smooth and uniformly convex Banach spaces. Finally, we give some applications of our theorem.