Strong convergence of perturbed Mann iteration for systems of variational inequality problems over the set of common fixed points of a finite family of demicontractive mappings in Banach spaces

In this paper, we propose an iterative algorithm, which is based on the Mann iterative method for solving simultaneously common fixed point problem with a finite family of demicontractive mappings and systems of variational inequalities involving an infinite family of strongly accretive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in Banach spaces. Application to systems of constrained convex minimization problem is provided to support our main results. The results of this paper improve and extend results of [M. Eslamian, C. R. Math. Acad. Sci. Paris, 355 (2017), 1168–1177], and of many others.