A New Class of Monotone Mappings and a New Class of Variational Inclusions in Banach Spaces

Abstract

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associated with this mappings and show its Lipschitz continuity. By using the technique of proximal mapping, we construct a new iterative algorithm. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known results.