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 Common Fixed Points for a Family of Quasi-φ-Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 754320 11 pages doi 2010 754320 Research Article Strong Convergence Theorems of Common Fixed Points for a Family of Quasi- -Nonexpansive Mappings Xiaolong Qin 1 Yeol Je Cho 2 Sun Young Cho 3 and Shin Min Kang4 1 Department of Mathematics Hangzhou Normal University Hangzhou 310036 China 2 Department of Mathematics Education and the RINS Gyeongsang National University Jinju 660-701 South Korea 3 Department of Mathematics Gyeongsang National University Jinju 660-701 South Korea 4 Department of Mathematics and the RINS Gyeongsang National University Jinju 660-701 South Korea Correspondence should be addressed to Shin Min Kang smkang@ Received 31 August 2009 Accepted 19 November 2009 Academic Editor Tomonari Suzuki Copyright 2010 Xiaolong Qin 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. We consider a modified Halpern type iterative algorithm for a family of quasi- -nonexpansive mappings in the framework of Banach spaces. Strong convergence theorems of the purposed iterative algorithms are established. 1. Introduction Let E be a Banach space C a nonempty closed and convex subset of E and T C C a nonlinear mapping. Recall that T is nonexpansive if Tx - Ty x - y Mx y e C. A point x e C is a fixed point of T provided Tx x. Denote by F T the set of fixed points of T that is F T x e C Tx x . 2 Fixed Point Theory and Applications One classical way to study nonexpansive mappings is to use contractions to approximate a nonexpansive mapping see 1 2 . More precisely take t e 0 1 and define a contraction Tt C C by Ttx tu 1 - t Tx Vx e C where u e C is a fixed element. Banach Contraction Mapping Principle guarantees that Tt has a unique fixed point xt in C. It is unclear in general what the behavior
