tailieunhanh - Báo cáo hóa học: " Research Article Strong Convergence Theorems by Shrinking Projection Methods for Class T Mappings"

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 by Shrinking Projection Methods for Class T Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 681214 7 pages doi 2011 681214 Research Article Strong Convergence Theorems by Shrinking Projection Methods for Class T Mappings Qiao-Li Dong 1 2 Songnian He 1 2 and Fang Su3 1 College of Science Civil Aviation University of China Tianjin 300300 China 2 Tianjin Key Laboratory for Advanced Signal Processing Civil Aviation University of China Tianjin 300300 China 3 Department of Mathematics and Systems Science National University of Defense Technology Changsha 410073 China Correspondence should be addressed to Qiao-Li Dong dongqiaoli@ Received 9 December 2010 Accepted 2 February 2011 Academic Editor S. Al-Homidan Copyright 2011 Qiao-Li Dong 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 prove a strong convergence theorem by a shrinking projection method for the class of T mappings. Using this theorem we get a new result. We also describe a shrinking projection method for a nonexpansive mapping on Hilbert spaces which is the same as that of Takahashi et al. 2008 . 1. Introduction Let H be a real Hilbert space with inner product and norm II II and let C be a nonempty closed convex subset of H. Recall that a mapping T H H is said to be nonexpansive if Tx- Ty x- y for all x y e H. The set of fixed points of T is Fix T x e H Tx x . T H H is said to be quasi-nonexpansive if Fix T is nonempty and Tx - p x - p for all x e H and p e Fix T . Given x y e H let H x y z e H z - y x - y 0 be the half-space generated by x y . A mapping T H H is said to be the class T or a cutter if T e T T H H dom T H and Fix T c H x Tx for all x e H . Remark . The class T is fundamental because it contains several types of operators commonly found in various areas of applied mathematics and in particular in .