Cayley approximation operator with an application to a system of set-valued Cayley type inclusions

Abstract

In this paper, we introduce and study a system of set-valued Cayley type inclusions involving Cayley operator and (H; )-monotone operator in real Banach spaces. We show that Cayley operator associated with the (H; )-monotone operator is Lipschitz type continuous. Using the proximal point operator technique, we have established a fixed point formulation for the system of set-valued Cayley type inclusions. Further, the existence and uniqueness of the approximate solution are proved. Moreover, we suggest an iterative algorithm for the system of set-valued Cayley type inclusions and discuss the strong convergence of the sequences generated by the proposed algorithm. Some examples are constructed to illustrate some concepts used in this paper.