M. A. Malik

In this paper, a new class of $H$-monotone in Banach spaces is considered and studied. The resolvent operator and Cayley approximation operator associated with the $H$-monotone are defined, and the Lipschitz continuity of Cayley approximation operator is also established. An application involves the solvability of a class of generalized Cayley inclusions with $H$-monotone in Banach spaces. By utilizing the technique of resolvent, an iterative algorithm is developed for solving such a class of generalized Cayley inclusions in Banach spaces. The convergence of the iterative sequence generated by the algorithm is proven under certain suitable conditions. The results are justified by means of a numerical example analytically and graphically using Python(matplotlib).