Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Strong Convergence Theorems of a New General Iterative Process with Meir-Keeler Contractions for a Countable Family of λi -Strict Pseudocontractions in q-Uniformly Smooth Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 354202 19 pages doi 2010 354202 Research Article Strong Convergence Theorems of a New General Iterative Process with Meir-Keeler Contractions for a Countable Family of Ấị-Strict Pseudocontractions in -Uniformly Smooth Banach Spaces Yanlai Song and Changsong Hu Department of Mathematics Hubei Normal University Huangshi 435002 China Correspondence should be addressed to Yanlai Song songyanlai2009@ Received 9 August 2010 Revised 2 October 2010 Accepted 14 November 2010 Academic Editor Mohamed Amine Khamsi Copyright 2010 Y. Song and C. Hu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We introduce a new iterative scheme with Meir-Keeler contractions for strict pseudocontractions in -uniformly smooth Banach spaces. We also discuss the strong convergence theorems for the new iterative scheme in q-uniformly smooth Banach space. Our results improve and extend the corresponding results announced by many others. 1. Introduction Throughout this paper we denote by E and E a real Banach space and the dual space of E respectively. Let C be a subset of E and lrt T be a non-self-mapping of C. We use F T to denote the set of fixed points of T. The norm of a Banach space E is said to be Gateaux differentiable if the limit x y - Hx lim------Z-T------ tF 0 t exists for all x y on the unit sphere S E x e E x 1 . If for each y e S E the limit is uniformly attained for x e S E then the norm of E is said to be uniformly Gateaux differentiable. The norm of E is said to be Frechet differentiable if for each x e S E the limit is attained uniformly for y e S E . The norm of E is said to be uniformly Frechet differentiable or uniformly smooth if the limit is attained uniformly for x y e S E X S E . 2 Fixed Point
