Iterative approximation of a solution of system of generalized nonlinear variational-like inclusions and a fixed point of total asymptotically nonexpansive mappings

Abstract

This paper investigates the problem of finding a point lying in the intersection of the set of solutions of a system of generalized nonlinear variational-like inclusions and the set of fixed points of a
total asymptotically nonexpansive mapping. To achieve this aim, a new iterative algorithm is suggested. Finally, the strong convergence and stability of the sequence generated by our proposed iterative algorithm to a common point of the above two sets are proved. The results presented in this paper are new, and improve and generalize many known corresponding results.