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 Relaxed Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of Strictly Pseudocontractive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 402602 16 pages doi 2009 402602 Research Article Relaxed Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of Strictly Pseudocontractive Mappings L. C. Ceng 1 David S. Shyu 2 and J. C. Yao3 1 Department of Mathematics Shanghai Normal University Shanghai 200234 China 2 Department of Finance National Sun Yat-Sen University Kaohsiung 80424 Taiwan 3 Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung 804 Taiwan Correspondence should be addressed to J. C. Yao yaojc@ Received 26 November 2008 Accepted 28 May 2009 Recommended by Lai-Jiu Lin We propose a relaxed composite implicit iteration process for finding approximate common fixed points of a finite family of strictly pseudocontractive mappings in Banach spaces. Several convergence results for this process are established. Copyright 2009 L. C. Ceng et al. 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. 1. Introduction and Preliminaries Let E be a real Banach space and let E be its dual space. Denote by J the normalized duality mapping from E into 2E defined by J x p e E x tp x 2 p 2Ị Vx e E where is the generalized duality pairing between E and E . If E is smooth then J is single valued and continuous from the norm topology of E to the weak topology of E . A mapping T with domain D T and range R T in E is called 1-strictly pseudocon-tractive in the terminology of Browder and Petryshyn 1 if there exists a constant 1 0 such that Tx - Ty j x - y Ilx - y 2 - Ã lx - y - Tx - Ty 2 2 Fixed Point Theory and Applications for all x y e D T and all j x - y e J x - y . Without loss of generality we may assume A e 0 1 . If I denotes the identity operator then can be written in the form I - T x
