Resolvent equation approach connected with H(.,.)-ϕ-η-mixed monotone mapping with an application

Abstract

The objective of this work is to use an application of H(.,.)-ϕ-η-mixed monotone mappings [13] via resolvent equation technique to solve the set-valued variational-like inclusions 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.