Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction
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 po...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/206515 |
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| author | Poom Kumam Fayyaz Rouzkard Mohammad Imdad Dhananjay Gopal |
| author_facet | Poom Kumam Fayyaz Rouzkard Mohammad Imdad Dhananjay Gopal |
| author_sort | Poom Kumam |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f10cc91b30ea4916a6b05d442b3aa35b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f10cc91b30ea4916a6b05d442b3aa35b2025-02-03T01:33:26ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/206515206515Fixed Point Theorems on Ordered Metric Spaces through a Rational ContractionPoom Kumam0Fayyaz Rouzkard1Mohammad Imdad2Dhananjay Gopal3Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bang Mod, Bangkok 10140, ThailandDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat 395007, IndiaRan 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.http://dx.doi.org/10.1155/2013/206515 |
| spellingShingle | Poom Kumam Fayyaz Rouzkard Mohammad Imdad Dhananjay Gopal Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction Abstract and Applied Analysis |
| title | Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction |
| title_full | Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction |
| title_fullStr | Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction |
| title_full_unstemmed | Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction |
| title_short | Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction |
| title_sort | fixed point theorems on ordered metric spaces through a rational contraction |
| url | http://dx.doi.org/10.1155/2013/206515 |
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