ITERATIVE SCHEME AND APPROXIMATION OF COMMON SOLUTIONS FOR VARIATIONAL INCLUSIONS AND FIXED POINT PROBLEMS

In this paper, we turn our attention to providing a new equivalence relation between the graph convergence of a sequence of P-eta-accretive mappings and their associated resolvent operators, respectively, to a given P-n-accretive mapping and its associated resolvent operator. With the goal of approximating a common element of the set of fixed points of a nearly asymptotically nonexpansive mapping and the set of solutions of a class of variational inclusions in a real Banach space setting, a new iterative algorithm is suggested using the resolvent operator technique. As an application of the obtained equivalence relationship, we also study the convergence analysis of the sequence generated by our proposed iterative algorithm. The final section is devoted to investigation and analysis of the concept of H(., .)-accretive operator and related results appeared in [X. Li, N.J. Huang, Graph convergence for the H(., .)-accretive operator in Banach spaces with an application, Appl. Math. Comput. 217 (2011) 9053-9061]. By pointing out some comments regarding H(.,.)-accretive operators, we show that the results given in the above-mentioned paper can be deduced as a special case of our main presented results.