Convergence Theorems for λ-strict Pseudo-contractions in q-uniformly Smooth Banach Spaces

<正> In this paper, we continue to discuss the 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.The results presented in this paper are interesting extensions and improvements upon those knownones of Marino and Xu [Marino, G., Xu, H. K.: Weak and strong convergence theorems for strictpseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 (2007)]. In order to geta strong convergence theorem, we modify the normal Mann's iterative algorithm by using a suitableconvex combination of a fixed vector and a sequence in C. This result extends a recent result of Kimand Xu [Kim, T. H., Xu, H. K.: Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51-60 (2005)] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spacesto q-uniformly smooth Banach spaces.