$H(.,.,.,.)$-$varphi$-$eta$-cocoercive Operator with an Application to Variational Inclusions

Abstract

In this work, we study generalized $ H(.,.,.,.)$-$varphi$-$eta-$ cocoercive operator to find the solution of variational like inclusion involving an infinite family of set-valued mappings in semi-inner product spaces via resolvent equation approach. Furthermore, we established an equivalence between the set-valued variational-like inclusion problem and fixed point problem by employing generalized resolvent operator technique involving generalized $H(.,.,.,.)$-$varphi$-$eta$-cocoercive operator. Using the equivalent formulation of set-valued variational-like inclusion problem and resolvent equation problem, an iterative algorithm is developed that approximate the uniqueness of solution of the resolvent equation problem.