(H(⋅,⋅),η)-accretive operators with an application for solving set-valued variational inclusions in Banach spaces

Abstract

In this paper, we introduce a new class of accretive operators— ( H ( ⋅ , ⋅ ) , η ) -accretive operators, which generalize many existing monotone or accretive operators. The resolvent operator associated with an ( H ( ⋅ , ⋅ ) , η ) -accretive operator is defined and its Lipschitz continuity is presented. By using the new resolvent operator technique, we also introduce and study a new class of set-valued variational inclusions involving ( H ( ⋅ , ⋅ ) , η ) -accretive operators and construct a new algorithm for solving this class of set-valued variational inclusions. These results are new, and improve and generalize many known corresponding results.