Fixed Point Results in Partial Symmetric Spaces with an Application
In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/1/13 |
| _version_ | 1818839957130706944 |
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| author | Mohammad Asim A. Rauf Khan Mohammad Imdad |
| author_facet | Mohammad Asim A. Rauf Khan Mohammad Imdad |
| author_sort | Mohammad Asim |
| collection | DOAJ |
| description | In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results. |
| first_indexed | 2024-12-19T04:02:32Z |
| format | Article |
| id | doaj.art-aac44a59df314ce7bb199cc5f64e9200 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-19T04:02:32Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-aac44a59df314ce7bb199cc5f64e92002022-12-21T20:36:38ZengMDPI AGAxioms2075-16802019-01-01811310.3390/axioms8010013axioms8010013Fixed Point Results in Partial Symmetric Spaces with an ApplicationMohammad Asim0A. Rauf Khan1Mohammad Imdad2Department of Mathematics, Aligarh Muslim University, Aligarh-202002, IndiaDepartment of Applied sciences, University Polytechnic, Aligarh Muslim University, Aligarh-202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002, IndiaIn this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results.https://www.mdpi.com/2075-1680/8/1/13partial symmetricfixed pointcontraction and weak contractionNadler’s theorem |
| spellingShingle | Mohammad Asim A. Rauf Khan Mohammad Imdad Fixed Point Results in Partial Symmetric Spaces with an Application Axioms partial symmetric fixed point contraction and weak contraction Nadler’s theorem |
| title | Fixed Point Results in Partial Symmetric Spaces with an Application |
| title_full | Fixed Point Results in Partial Symmetric Spaces with an Application |
| title_fullStr | Fixed Point Results in Partial Symmetric Spaces with an Application |
| title_full_unstemmed | Fixed Point Results in Partial Symmetric Spaces with an Application |
| title_short | Fixed Point Results in Partial Symmetric Spaces with an Application |
| title_sort | fixed point results in partial symmetric spaces with an application |
| topic | partial symmetric fixed point contraction and weak contraction Nadler’s theorem |
| url | https://www.mdpi.com/2075-1680/8/1/13 |
| work_keys_str_mv | AT mohammadasim fixedpointresultsinpartialsymmetricspaceswithanapplication AT araufkhan fixedpointresultsinpartialsymmetricspaceswithanapplication AT mohammadimdad fixedpointresultsinpartialsymmetricspaceswithanapplication |