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.