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: Fixed point results for contractions involving generalized altering distances in ordered metric spaces | Nashine et al. Fixed Point Theory and Applications 2011 2011 5 http content 2011 1 5 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Fixed point results for contractions involving generalized altering distances in ordered metric spaces Hemant Kumar Nashine 1 Bessem Samet2 and Jong Kyu Kim3 Correspondence jongkyuk@ department of Mathematics Kyungnam University Masan Kyungnam 631-701 Korea Full list of author information is available at the end of the article SpringerOpen0 Abstract In this article we establish coincidence point and common fixed point theorems for mappings satisfying a contractive inequality which involves two generalized altering distance functions in ordered complete metric spaces. As application we study the existence of a common solution to a system of integral equations. 2000 Mathematics subject classification. Primary 47H10 Secondary 54H25 Keywords Coincidence point Common fixed point Complete metric space Generalized altering distance function Weakly contractive condition Weakly increasing Partially ordered set Introduction and Preliminaries There are a lot of generalizations of the Banach contraction-mapping principle in the literature see 1-31 and others . A new category of contractive fixed point problems was addressed by Khan et al. 1 . In this study they introduced the notion of an altering distance function which is a control function that alters distance between two points in a metric space. Definition . 1 A function Ộ 0 0 is called an altering distance function if the following conditions are satisfied. i Ộ is continuous. ii Ộ is non-decreasing. iii f t 0 t 0. Khan et al. 1 proved the following result Theorem . 1 Let X d be a complete metric space f. 0 0 be an altering distance function and T X X be a self-mapping which satisfies the following inequality p d Tx Ty O f d x y for all x y e X and for some 0 c 1. Then T has a unique fixed point.
