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 Generalized Weakly Contractive Condition in Ordered Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 132367 20 pages doi 2011 132367 Research Article Fixed Point Theorems for Generalized Weakly Contractive Condition in Ordered Metric Spaces Hemant Kumar Nashine1 and Ishak Altun2 1 Department of Mathematics Disha Institute of Management and Technology Satya Vihar Vidhansabha-Chandrakhuri Marg Mandir Hasaud Raipur 492101 Chhattisgarh India 2 Department of Mathematics Faculty of Science and Arts Kirikkale University 71450 Yahsihan Kirikkale Turkey Correspondence should be addressed to Ishak Altun ishakaltun@ Received 30 September 2010 Accepted 11 February 2011 Academic Editor Yeol J. Cho Copyright 2011 H. K. Nashine and I. Altun. 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. Fixed point results with the concept of generalized weakly contractive conditions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature. 1. Introduction and Preliminaries There are a lot of generalizations of the Banach contraction mapping principle in the literature. One of the most interesting of them is the result of Khan et al. 1 . They addressed a new category of fixed point problems for a single self-map with the help of a control function which they called an altering distance function. A function p 0 to 0 to is called an altering distance function if p is continuous nondecreasing and 0 0 holds. Khan et al. 1 given the following result. Theorem . Let X d be a complete metric space let y be an altering distance function and let T X X be a self-mapping which satisfies the following inequality y d Tx Ty cq d x y for all x y e X and for some 0 c 1. Then T has a unique fixed point. 2 Fixed Point Theory and Applications In fact Khan et al. 1 proved a .
