The main contributions of this paper is twofold. First, our primary concern is to suggest a new iterative algorithm using the P-η-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(., .)-η-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(., .)-η-cocoercive mapping, every H(., .)-η-cocoercive mapping is P-η-accretive and is not a new one is pointed out. At the same time, some important comments on H(., .)-η-cocoercive mapping and the results given in the above-mentioned paper are stated.