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

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 establish its equivalence with fixed point problems the help concept (H, ?)-proximal mapping. The obtained alternative equivalent formulation used iterative algorithm for finding approximate solution proposed. Under some appropriate assumptions imposed on mappings parameters involved inclusions, existence mentioned above proved convergence analysis sequences generated by our suggested discussed. second objective paper investigate analyze notion Cn-?-monotone mapping, which an extension Cn-monotone out remarks relating mapping results concerning it appeared literature. presented are new, improve generalize many known corresponding results.