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Báo cáo hóa học: " Research Article A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces Urailuk Singthong1 and Suthep Suantai1, 2"

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 A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces Urailuk Singthong1 and Suthep Suantai1, 2 | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 262691 12 pages doi 10.1155 2010 262691 Research Article A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces Urailuk Singthong1 and Suthep Suantai1 2 1 Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand 2 PERDO National Centre of Excellence in Mathematics Faculty of Science Mahidol University Bangkok 10400 Thailand Correspondence should be addressed to Suthep Suantai scmti005@chiangmai.ac.th Received 10 February 2010 Revised 21 June 2010 Accepted 15 July 2010 Academic Editor Massimo Furi Copyright 2010 U. Singthong and S. Suantai. 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 general iterative method by using the X-mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others. 1. Introduction Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. A mapping T of C into itself is called nonexpansive if II Tx - Ty x - y for all x y e C. A point x e C is called a fixed point of T provided that Tx x. We denote by F T the set of fixed points of T i.e. F T x e H Tx x . Recall that a self-mapping f C C is a contraction on C if there exists a constant a e 0 1 such that Wfx - fy a x - y for all x y e C. A bounded linear operator A on H is called strongly positive with coefficient Y if there is a constant Y 0 with the property Ax x Y x 2 Vx e H. 1.1 In 1953 Mann 1 introduced a well-known classical iteration to approximate a fixed point of a nonexpansive .