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The aim of this paper is to introduce a new H(⋅,⋅)Open image in new window-η-cocoercive operator and its resolvent operator. We study some of the properties of H(⋅,⋅)Open image in new window-η-cocoercive operator and prove the Lipschitz continuity of resolvent operator associated with H(⋅,⋅)Open image in new window-η-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(⋅,⋅)Open image in new window-η-cocoercive operator.

journal of inequalities and applications

Generalized set-valued variational-like inclusions involving "Equation missing" -η-cocoercive operator in Banach spaces

Generalized set-valued variational-like inclusions involving "Equation missing" -η-cocoercive operator in Banach spaces