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The purpose of this paper is to study existence and approximation of solutions of system of variational inclusions involving multi-valued H-accretive and single-valued accretive operators over two different closed convex subsets of a Banach space. The convergence analysis of two proposed iteration processes for approximating solutions will be conducted within the conceptual framework of the ''altering point technique'' without uniform convexity of underlying spaces. This technique should make existing or new results in solving system of variational inequalities and variational inclusions. [ABSTRACT FROM AUTHOR]

The Mann iterates behave well for nonexpansive mappings for any initial guess in the domain. Our aim in this article is to extend this method to a broad class of inexact fixed point algorithms generated by nearly nonexpansive sequences in Banach spaces and to locate the weak limit of the iterates by its initial guesses. Due to the inexactness, our algorithms become efficiently applicable for a wider class of problems. As applications, we give convergence theorems for finding solutions of variational inclusion problems and constrained multiple-sets split feasibility problems. Our results are significant refinements and improvements of the corresponding results in the literature. [ABSTRACT FROM AUTHOR]