Convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces

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 cl-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-con tractions in Hilbert spaces. Nonlinear Anal. 67 (2007) 2258-2271] and Zhou [H. Zhou, Convergence theorems for lambda-strict pseudo-contractions in 2-uniformly smooth Banach spaces, Nonlinear Anal. 69 (2008) 3160-3173]. (C) 2009 Elsevier Ltd. All rights reserved.