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 Generalized Asymptotic Pointwise Contractions and Nonexpansive Mappings Involving Orbits Adriana Nicolae | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 458265 19 pages doi 2010 458265 Research Article Generalized Asymptotic Pointwise Contractions and Nonexpansive Mappings Involving Orbits Adriana Nicolae Department of Applied Mathematics Babeậ-Bolyai University Kogalniceanu 1 400084 Cluj-Napoca Romania Correspondence should be addressed to Adriana Nicolae anicolae@ Received 30 September 2009 Accepted 25 November 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 Adriana Nicolae. 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 give fixed point results for classes of mappings that generalize pointwise contractions asymptotic contractions asymptotic pointwise contractions and nonexpansive and asymptotic nonexpansive mappings. We consider the case of metric spaces and in particular CAT 0 spaces. We also study the well-posedness of these fixed point problems. 1. Introduction Four recent papers 1-4 present simple and elegant proofs of fixed point results for pointwise contractions asymptotic pointwise contractions and asymptotic nonexpansive mappings. Kirk and Xu 1 study these mappings in the context of weakly compact convex subsets of Banach spaces respectively in uniformly convex Banach spaces. Hussain and Khamsi 2 consider these problems in the framework of metric spaces and CAT 0 spaces. In 3 the authors prove coincidence results for asymptotic pointwise nonexpansive mappings. Espinola et al. 4 examine the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. In this paper we do not consider more general spaces but instead we formulate less restrictive conditions for the mappings and show that the conclusions of the theorems still stand even in such weaker settings. .