Generalized Cayley operator with applications to Cayley inclusions in uniformly smooth Banach spaces

Abstract

In this paper, we present a generalized Cayley operator and a generalized Cayley inclusion problem $ (GCIP) $. A fixed point formulation of $ (GCIP) $ is established and using this an iterative algorithm is developed to show the existence and convergence of the solutions of $ (GCIP) $. We also establish the equivalence of the $ (GCIP) $ and generalized resolvent equation problem $ (GREP) $, and develop an iterative algorithm and some of its equivalent forms to approximate the solution of $ (GREP) $. To support our results, we construct a numerical example and convergence graphs using MATLAB programming.