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 Fixed Point Iterations of a Pair of Hemirelatively Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 270150 14 pages doi 2010 270150 Research Article Fixed Point Iterations of a Pair of Hemirelatively Nonexpansive Mappings Yan Hao1 2 and Sun Young Cho3 1 School of Mathematics Physics and Information Science Zhejiang Ocean University Zhoushan 316004 China 2 College of Mathematics Physics and Information Engineering Zhejiang Normal University Jinhua 321004 China 3 Department of Mathematics Gyeongsang National University Jinju 660-701 South Korea Correspondence should be addressed to Yan Hao zjhaoyan@ Received 27 September 2009 Accepted 22 March 2010 Academic Editor Tomonari Suzuki Copyright 2010 Y. Hao and S. Y. Cho. 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 an iterative method for a pair of hemirelatively nonexpansive mappings. Strong convergence of the purposed iterative method is obtained in a Banach space. 1. Introduction and Preliminaries Let E be a Banach space with the dual E . We denote by J the normalized duality mapping from E to 2E defined by Jx f e E x f x 2 117 112 where denotes the generalized duality pairing. A Banach space E is said to be strictly convex if II x y 2 1 for all x y e E with xH llyll 1 and x fy. It is said to be uniformly convex if limn ix - yn 0 for any two sequences xn and yn in E such that xnH yn 1 and limn lix yn 2 1. Let UE x e E xH 1 be the unit sphere of E. Then the Banach space E is said to be smooth provided that lim Ilx tyịị - llxQ t o i 2 Fixed Point Theory and Applications exists for each x y e Ue. It is also said to be uniformly smooth if the limit is attained uniformly for x y e Ue . It is well known that if E is uniformly smooth then J is uniformly norm-to-norm continuous on each bounded subset of E. It is also well known that
