Variational-like inclusion involving infinite family of set-valued mappings governed by resolvent equations

Abstract

The purpose of this work is to investigate generalized H(.,.,.)-ϕ-η-cocoercive operator and use its application via resolvent equation approach to solve the variational-like inclusion involving infinite family of set-valued mappings in semi-inner product spaces. We aim to establish an equivalence between the set-valued variational-like inclusion problem and fixed point problem. A relationship also obtain between the set-valued variational-like inclusion problem and the resolvent equation problem. This equivalent formulation suggests an idea to construct an iterative algorithm to find a solution of the resolvent equation problem.