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Báo cáo hóa học: " Research Article Fixed Point Theorems for Monotone Mappings on Partial 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 Theorems for Monotone Mappings on Partial Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 508730 10 pages doi 10.1155 2011 508730 Research Article Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces Ishak Altun and Ali Erduran Department of Mathematics Faculty of Science and Arts Kirikkale University 71450 Yahsihan Kirikkale Turkey Correspondence should be addressed to Ishak Altun ishakaltun@yahoo.com Received 12 November 2010 Accepted 24 December 2010 Academic Editor S. Al-Homidan Copyright 2011 I. Altun and A. Erduran. 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. Matthews 1994 introduced a new distance p on a nonempty set X which is called partial metric. If X p is a partial metric space then p x x may not be zero for x e X. In the present paper we give some fixed point results on these interesting spaces. 1. Introduction There are a lot of fixed and common fixed point results in different types of spaces. For example metric spaces fuzzy metric spaces and uniform spaces. One of the most interesting is partial metric space which is defined by Matthews 1 . In partial metric spaces the distance of a point in the self may not be zero. After the definition of partial metric space Matthews proved the partial metric version of Banach fixed point theorem. Then Valero 2 Oltra and Valero 3 and Altun et al. 4 gave some generalizations of the result of Matthews. Again Romaguera 5 proved the Caristi type fixed point theorem on this space. First we recall some definitions of partial metric spaces and some properties of theirs. See 1-3 5-7 for details. A partial metric on a nonempty set X is a function p X X X R such that for all x y z e X p1 x y o p x x p x y p y y p2 p x x p x y 2 Fixed Point Theory and Applications pa p x y p y x p4 p x y p x z p z y - p z z . A partial metric space is a pair X p