Best Proximity Point Results for Modified --Proximal Rational Contractions
We first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixe...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/927457 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556709497798656 |
|---|---|
| author | N. Hussain M. A. Kutbi P. Salimi |
| author_facet | N. Hussain M. A. Kutbi P. Salimi |
| author_sort | N. Hussain |
| collection | DOAJ |
| description | We first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to
illustrate the usability of the obtained results. |
| format | Article |
| id | doaj-art-d705fec9566f4931a0d3a637eaa461a6 |
| 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-d705fec9566f4931a0d3a637eaa461a62025-02-03T05:44:41ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/927457927457Best Proximity Point Results for Modified --Proximal Rational ContractionsN. Hussain0M. A. Kutbi1P. Salimi2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Astara Branch, Islamic Azad University, Astara, IranWe first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.http://dx.doi.org/10.1155/2013/927457 |
| spellingShingle | N. Hussain M. A. Kutbi P. Salimi Best Proximity Point Results for Modified --Proximal Rational Contractions Abstract and Applied Analysis |
| title | Best Proximity Point Results for Modified --Proximal Rational Contractions |
| title_full | Best Proximity Point Results for Modified --Proximal Rational Contractions |
| title_fullStr | Best Proximity Point Results for Modified --Proximal Rational Contractions |
| title_full_unstemmed | Best Proximity Point Results for Modified --Proximal Rational Contractions |
| title_short | Best Proximity Point Results for Modified --Proximal Rational Contractions |
| title_sort | best proximity point results for modified proximal rational contractions |
| url | http://dx.doi.org/10.1155/2013/927457 |
| work_keys_str_mv | AT nhussain bestproximitypointresultsformodifiedproximalrationalcontractions AT makutbi bestproximitypointresultsformodifiedproximalrationalcontractions AT psalimi bestproximitypointresultsformodifiedproximalrationalcontractions |