h(., ., ., .)-ϕ-η-cocoercive operator with an application to variational inclusions

This paper deals with the 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. applying the generalized resolvent operator tech nique involving generalized h (., ., ., .)-ϕ-η-cocoercive operator, an equivalence between the set-valued variational-like inclusion problem and fixed point problem is established. a relationship between the set-valued variational-like inclusion problem and resolvent equation is also established. using this equivalent formulation an iterative algorithm is developed that approximate the unique solution of the resolvent equation.