(H,ϕ)-η-monotone operators in Banach spaces with an application to variational inclusions

In this paper, we introduce and study a new class of (H,ϕ)-η-monotone operators in Banach spaces. We define a proximal mapping associated with the (H,ϕ)-η-monotone operator and show its Lipschitz continuity. As an application, we consider the solvability for a class of variational inclusions involving the (H,ϕ)-η-monotone operators in Banach spaces. By using the technique of proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm.