Multi-valued Variational Inclusion Problem and Convergence Analysis

Abstract

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a $(\widehat{H},\eta)$-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. The resolvent operator method is used and a new equivalence relationship between a class of multi-valued variational inclusion problems involving $(\widehat{H},\eta)$-monotone operators and a class of fixed points problems is established. The obtained equivalence relationship is employed and a new iterative algorithm for solving the multi-valued variational inclusion problem is constructed. Under some suitable assumptions, the convergence analysis of the sequences generated by our proposed iterative algorithm is studied.