Convergence theorems for strict pseudo-contractions in [formula omitted]-uniformly smooth Banach spaces

Abstract

In this paper, we discuss some properties of iterates generated by a strict pseudo-contraction or a finite family of strict pseudo-contractions in a real q -uniformly smooth Banach space. We prove the weak convergence and strong convergence of pseudo-contractive mappings. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–349], Acedo and Xu [G.L. Acedo, H.K. Xu, Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 67 (2007) 2258–2271] and Zhou [H. Zhou, Convergence theorems for λ -strict pseudo-contractions in 2-uniformly smooth Banach spaces, Nonlinear Anal. 69 (2008) 3160–3173].