Generalized variational inclusions and H-resolvent equations with H-accretive operators

Abstract

In this paper, we consider a more general form of variational inclusions, called generalized variational inclusion (for short, GVI). In connection with GVI, we also consider a generalized resolvent equation with H-resolvent operator, called H-resolvent equation (for short, H-RE). We suggest iterative algorithms to compute the approximate solutions of GVI and H-RE. The existence of a unique solution of GVI and H-RE and convergence of iterative sequences generated by the proposed algorithms are also studied. Several special cases are also discussed.