An algorithmic approach for a system of extended multi-valued variational-like inclusions in Banach spaces

Abstract

In this paper, we pursue two purposes. Our first goal is to study a new system of extended multi-valued nonlinear variational inclusions in Banach spaces and to establish its equivalence with a system of fixed point problems with the help of the concept of (H, ?)-proximal mapping. The obtained alternative equivalent formulation is used and a new iterative algorithm for finding its approximate solution is proposed. Under some appropriate assumptions imposed on the mappings and parameters involved in the system of extended multi-valued nonlinear variational inclusions, the existence of solution for the system mentioned above is proved and the convergence analysis of the sequences generated by our suggested iterative algorithm is discussed. The second objective of this paper is to investigate and analyze the notion of Cn-?-monotone mapping, which is an extension of the concept of Cn-monotone mapping, and to point out some remarks relating to Cn-?-monotone mapping and the results concerning it appeared in the literature. The results presented in this paper are new, and improve and generalize many known corresponding results.