TAILIEUCHUNG - Báo cáo hóa học: " Research Article Generalized Caristi’s Fixed Point Theorems"

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 Caristi’s Fixed Point Theorems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 170140 7 pages doi 2009 170140 Research Article Generalized Caristi s Fixed Point Theorems Abdul Latif Department of Mathematics King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Abdul Latif latifmath@ Received 27 December 2008 Accepted 9 February 2009 Recommended by Mohamed A. Khamsi We present generalized versions of Caristi s fixed point theorem for multivalued maps. Our results either improve or generalize the corresponding generalized Caristi s fixed point theorems due to Bae 2003 Suzuki 2005 Khamsi 2008 and others. Copyright 2009 Abdul Latif. 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. 1. Introduction A number of extensions of the Banach contraction principle have appeared in literature. One of its most important extensions is known as Caristi s fixed point theorem. It is well known that Caristi s fixed point theorem is equivalent to Ekland variational principle 1 which is nowadays an important tool in nonlinear analysis. Many authors have studied and generalized Caristi s fixed point theorem to various directions. For example see 28 . Kada et al. 9 and Suzuki 10 introduced the concepts of -distance and T-distance on metric spaces respectively. Using these generalized distances they improved Caristi s fixed point theorem and Ekland variational principle for single-valued maps. In this paper using the concepts of -distance and T -distance we present some generalizations of the Caristi s fixed point theorem for multivalued maps. Our results either improve or generalize the corresponding results due to Bae 4 11 Kada et al. 9 Suzuki 8 10 Khamsi 5 and many of others. Let X be a metric space with metric d. We use 2X to denote the collection .

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