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The main purpose of this paper is to construct a new iterative algorithm using the notion of  P - η -resolvent operator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved.

Algorithmic Aspect and Iterative Approximation of a Solution for a System of Generalized Multi-Valued Variational-Like Inclusions in Banach Spaces