Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces

Abstract

Abstract In this paper, we consider a type of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces that are the sum of monotone operators and fixed point problems. By assuming the existence of solutions, we provide a suitable algorithm for finding a solution point. Some important applications and numerical experiments of the considered problem and constructed algorithm are also discussed.

Keywords

• split feasibility problems
• maximal monotone operators
• inverse strongly monotone operator
• fixed point problems
• weak convergence theorems