GRAPH CONVERGENCE AND GENERALIZED CAYLEY OPERATOR WITH AN APPLICATION TO A SYSTEM OF CAYLEY INCLUSIONS IN SEMI-INNER PRODUCT SPACES

Abstract

In this paper, we introduce and study a generalized Cayley operator associated to H(·,·)-monotone operator in semi-inner product spaces. Using the notion of graph convergence, we give the equivalence result between graph convergence and convergence of generalized Cayley operator for the H(·, ·)-monotone operator without using the convergence of the associated resolvent operator. To support our claim, we construct a numerical example. As an application, we consider a system of generalized Cayley inclusions involving H(·,·)-monotone operators and give the existence and uniqueness of the solution for this system. Finally, we propose a perturbed iterative algorithm for finding the approximate so- lution and discuss the convergence of iterative sequences generated by the perturbed iterative algorithm.