Approximating solutions for the systems of strongly accretive operator equations

The purpose of this paper is to study a strong convergence of multi-step iterative scheme to a common fixed point for a finite family of strongly pseudo-contractive mappings. As a consequence, the strong convergence theorems for the modified multi-step iterative sequence to a solution of systems of strongly accretive operator equations are obtained in real uniformly smooth Banach spaces. The results presented in this paper improve and extend the corresponding Xu [Y. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91–101] and Noor, Rassias and Huang [M.A. Noor, T.M. Rassias, Z. Huang, Three-step iterations for nonlinear accretive operator equations, J. Math. Anal. Appl. 274 (2002) 59–68], and many others.