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 Approximating Fixed Points of Non-Lipschitzian Mappings by Metric Projections | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 976192 9 pages doi 2011 976192 Research Article Approximating Fixed Points of Non-Lipschitzian Mappings by Metric Projections Hossein Dehghan 1 Amir Gharajelo 2 and Davood Afkhamitaba3 1 Department of Mathematics Institute for Advanced Studies in Basic Sciences IASBS Gava Zang Zanjan 45137-66731 Iran 2 Department of Mathematics Roozbeh Institute of Higher Education Zanjan 45186-74947 Iran 3 Department of Mathematics Bandar Abbas Branch Islamic Azad University Bandar Abbas 79158-93144 Iran Correspondence should be addressed to Hossein Dehghan h-dehghan@ Received 22 November 2010 Revised 5 February 2011 Accepted 8 February 2011 Academic Editor Naseer Shahzad Copyright 2011 Hossein Dehghan 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 define and study a new iterative algorithm inspired by Matsushita and Takahashi 2008 . We establish a strong convergence theorem of the proposed algorithm for asymptotically nonexpansive in the intermediate sense mappings in uniformly convex and smooth Banach spaces by using metric projections. This theorem generalizes and refines Matsushita and Takahashi s strong convergence theorem which was established for nonexpansive mappings. 1. Introduction and Preliminaries Let E be a real Banach space and let C be a nonempty subset of E. A mapping T C C is said to be asymptotically nonexpansive if there exists a sequence kn in 1 to with 1 such that Tnx - TnyW k Wx - yll for all x y e C and each n 1. If kn 1 then T is known as nonexpansive mapping. T is said to be asymptotically nonexpansive in the intermediate sense 1 provided T is uniformly continuous and limsupsup Tnx - TnyW - x - yll 0. n to x yeC 2 Fixed Point Theory and Applications T is said .
