Fixed Point Theorems for Manageable Contractions with Application to Integral Equations
In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/7943896 |
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| _version_ | 1832550662600130560 |
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| author | N. Hussain I. Iqbal Badriah A. S. Alamri M. A. Kutbi |
| author_facet | N. Hussain I. Iqbal Badriah A. S. Alamri M. A. Kutbi |
| author_sort | N. Hussain |
| collection | DOAJ |
| description | In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations. |
| format | Article |
| id | doaj-art-dd7d954aa1f3486c9b7db95a8a5e894b |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-dd7d954aa1f3486c9b7db95a8a5e894b2025-02-03T06:06:18ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/79438967943896Fixed Point Theorems for Manageable Contractions with Application to Integral EquationsN. Hussain0I. Iqbal1Badriah A. S. Alamri2M. A. Kutbi3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment 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 ArabiaIn this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.http://dx.doi.org/10.1155/2017/7943896 |
| spellingShingle | N. Hussain I. Iqbal Badriah A. S. Alamri M. A. Kutbi Fixed Point Theorems for Manageable Contractions with Application to Integral Equations Journal of Function Spaces |
| title | Fixed Point Theorems for Manageable Contractions with Application to Integral Equations |
| title_full | Fixed Point Theorems for Manageable Contractions with Application to Integral Equations |
| title_fullStr | Fixed Point Theorems for Manageable Contractions with Application to Integral Equations |
| title_full_unstemmed | Fixed Point Theorems for Manageable Contractions with Application to Integral Equations |
| title_short | Fixed Point Theorems for Manageable Contractions with Application to Integral Equations |
| title_sort | fixed point theorems for manageable contractions with application to integral equations |
| url | http://dx.doi.org/10.1155/2017/7943896 |
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