Algorithmic Aspect and Convergence Analysis for System of Generalized Multivalued Variational-like Inequalities

The main aim of this paper is twofold. Our first objective to study a new system generalized multivalued variational-like inequalities in Banach spaces and establish its equivalence with fixed point problems utilizing the concept P-?-proximal mapping. obtained alternative equivalent formulation used iterative algorithm for finding approximate solution suggested. Under some appropriate assumptions imposed on mappings parameters involved inequalities, existence mentioned above proved convergence analysis sequences generated by our proposed discussed. second work investigate analyze notion M-?-proximal mapping defined literature. Taking into account considered such mapping, we prove that every actually not one. At same time, comments relating existing results are pointed out.