Modified Inertial Algorithms for a Class of Split Feasibility Problems and Fixed Point Problems in Hilbert Spaces

Abstract

In this work, we introduce an iterative algorithm for solving the split feasibility problem on zeros of the sum of monotone operators and fixed point sets and also solving the fixed point problem of a nonexpansive mapping. This algorithm is a modification of the method based on the inertial and Mann viscosity-type methods. By assuming the existence of solutions, we show the strong convergence theorems of the constructed sequences. Finally, we also apply the proposed algorithm to related problems in Hilbert spaces.

Keywords

• split feasibility problem
• fixed point problem
• maximal monotone operator
• convergence theorems