An accelerated Tseng type method for solving zero point problems and certain optimization problems

Abstract

In this paper, we proposed a modified Tseng’s splitting iterative algorithm for approximating a solution of split feasibility problem for zero and fixed point problems. By incorporating an inertial extrapolation method and Halpern iterative technique, we established a strong convergence result for approximating a solution of split fixed point problem for a nonexpansive and quasinonexpansive mapping which is also a zero point of sum of two monotone operators in the framework of real Hilbert spaces. Furthermore, we present a numerical example to support our main result. The results obtained in this paper improve, extend and unify some related results in the literature.