Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction. (22nd August 2013)

• Record Type: Journal Article
• Authors: Kumam, Poom; Rouzkard, Fayyaz; Imdad, Mohammad; Gopal, Dhananjay
• Other Names: Hernandez Salvador Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-08-22
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/206515
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Ran and Reurings (2004) established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.