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