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KeyWord:System of variational-like inclusion problems; $(H,\varphi)-\eta$-monotone mappings; Resolvent operator; Cocoercive mappings; Banach spaces
In this manuscript, by using $(H,\varphi)-\eta$-monotone operators we study the existence of solution of a system of variational-like inclusion problems in Banach spaces. Further, we suggest an iterative algorithm for finding the approximate solution of this system and discuss the convergence criteria of the sequences generated by the iterative algorithm. The method used in this paper can be considered as an extension of methods for studying the existence of solution for various classes of variational inclusions considered and studied by many authors in Banach spaces.