Algorithmic and analytical approach of solutions of a system of generalized multi-valued nonlinear variational inclusions

The main contributions of this paper is twofold. First, our primary concern to suggest a new iterative algorithm using the P-?-proximal-point mapping technique and Nadler?s for finding approximate solutions system generalized multi-valued nonlinear variational-like inclusions. Under some appropriate conditions imposed on parameters mappings involved in inclusions, strong convergence sequences generated by proposed solution aforesaid proved. Second, H(.,.)-?-cocoercive considered [R. Ahmad, M. Dilshad, Akram, Resolvent operator solving inclusions Banach sapces, Filomat 26(5)(2012) 897- 908] investigated analyzed, fact that under assumptions H(., .)-?-cocoercive mapping, every P-?-accretive not one pointed out. At same time, important comments results given above-mentioned are stated.