Generalized set-valued variational-like inclusions involving H(.,.)-η-cocoercive operator in Banach spaces

The aim of this paper is to introduce a new H(., .)-eta-cocoercive operator and its resolvent operator. We study some of the properties of H(., .)-eta-cocoercive operator and prove the Lipschitz continuity of resolvent operator associated with H(., .)-eta-cocoercive operator. Finally, we apply the techniques of resolvent operator to solve a generalized set-valued variational-like inclusion problem in Banach spaces. Our results are new and generalize many known results existing in the literature. Some examples are given in support of definition of H(., .)-eta-cocoercive operator.