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báo cáo hóa học:" Research Article Fixed Point and Best Proximity Theorems under Two Classes of Integral-Type Contractive Conditions in Uniform Metric Spaces"

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 and Best Proximity Theorems under Two Classes of Integral-Type Contractive Conditions in Uniform Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 510974 12 pages doi 10.1155 2010 510974 Research Article Fixed Point and Best Proximity Theorems under Two Classes of Integral-Type Contractive Conditions in Uniform Metric Spaces M. De la Sen Institute of Research and Development of Processes University of the Basque Country Campus ofLeioa Bizkaia P.O. Box. 644- Bilbao 48080 Bilbao Spain Correspondence should be addressed to M. De la Sen manuel.delasen@ehu.es Received 5 July 2010 Accepted 14 October 2010 Academic Editor S. Reich Copyright 2010 M. De la Sen. 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. This paper investigates the existence of fixed points and best proximity points of p-cyclic selfmaps on a set of subsets of a certain uniform space under integral-type contractive conditions. The parallel properties of the associated restricted composed maps from any of the subsets to itself are also investigated. The subsets of the uniform space are not assumed to intersect. 1. Introduction Fixed point theory is of an intrinsic theoretical interest but also a useful tool in a wide class of practical problems. There is an exhaustive variety of results concerning fixed point theory in Banach spaces and metric spaces involving different types of contractive conditions including those associated with the so-called Kannan maps and with Meir-Keeler contractions see e.g. 1-6 . There is also a rich background literature concerning the use of contractive conditions in integral form using altering distances Lebesgue integrable test functions and comparison functions 7-9 . Also the so-called reasonable expansive mappings have been investigated in 10 and conditions for the existence of fixed points have been given. It has been used for instance for the study of the Lyapunov .