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 Points for Pseudocontractive Mappings on Unbounded Domains | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 769858 17 pages doi 2010 769858 Research Article Fixed Points for Pseudocontractive Mappings on Unbounded Domains Jesus Garcia-Falset and E. Llorens-Fuster Departamento de Analisis Matemdtico Facultad de Matemdticas Universitat de Valencia 46100 Burjassot Spain Correspondence should be addressed to JesUs Garcia-Falset garciaf@ Received 4 September 2009 Accepted 14 October 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 J. Garcia-Falset and E. Llorens-Fuster. 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 some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot Isac and Nemeth. An application to integral equations is given. 1. Introduction Let C be a nonempty subset of a Banach space X with norm II II. Recall that a mapping T C X is said to be nonexpansive whenever IIT x - T y 11 II x - y II for every x y e C. X is said to have the fixed point property FPP for short if every nonexpansive selfmapping of each nonempty bounded closed and convex subset of X has a fixed point. It has been known from the outset of the study of this property around the early sixties of the last century that it depends strongly on nice geometrical properties of the space. For instance a celebrated result due to Kirk 1 establishes that those reflexive Banach spaces with normal structure NS have the FPP . In particular uniformly convex Banach spaces have normal structure see 2 3 for more information . If C is a closed convex of a Banach space enjoying the FPP in general it is not true that T C C has a fixed point due to the possible unboundedness of C it is enough to consider any translation map with nonnull vector .