(H(·,·), η)-MONOTONE OPERATOR WITH AN APPLICATION TO A SYSTEM OF SET-VALUED VARIATIONAL-LIKE INCLUSIONS IN BANACH SPACES

Abstract

In this paper, we introduce and study a new class of (H(.,.),η)-monotone operator in Banach spaces. We define the generalized η-proximal operator associated with (H(., .), η)-monotone operator and show its Lipschitz continuity. As an application, we consider the generalized system of variational-like inclusions involving (H(., .), η)-monotone operators in Banach spaces and by using proximal operator technique, we construct an iterative algorithm for solving this system. Also, we prove the existence of solution and discuss the convergence analysis of the iterative algorithm for the generalized system of variationallike inclusions. The theorems presented in this paper improve and generalize many known results in the literature.