Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications
Motivated by the ideas of F-weak contractions and F,Rg-contractions, the notion of Fw,Rg-contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an ad...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9937318 |
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| _version_ | 1832546039983243264 |
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| author | Muhammad Aslam Hassen Aydi Samina Batul Amna Naz |
| author_facet | Muhammad Aslam Hassen Aydi Samina Batul Amna Naz |
| author_sort | Muhammad Aslam |
| collection | DOAJ |
| description | Motivated by the ideas of F-weak contractions and F,Rg-contractions, the notion of Fw,Rg-contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for Fw,Rg-contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated. |
| format | Article |
| id | doaj-art-1359405fd3dd49e9a83a71c34c9a6328 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-1359405fd3dd49e9a83a71c34c9a63282025-02-03T07:23:53ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/99373189937318Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and ApplicationsMuhammad Aslam0Hassen Aydi1Samina Batul2Amna Naz3Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi ArabiaUniversité de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse, 4000, TunisiaDepartment of Mathematics, Capital University of Science and Technology, Islamabad, PakistanDepartment of Mathematics, Capital University of Science and Technology, Islamabad, PakistanMotivated by the ideas of F-weak contractions and F,Rg-contractions, the notion of Fw,Rg-contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for Fw,Rg-contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.http://dx.doi.org/10.1155/2021/9937318 |
| spellingShingle | Muhammad Aslam Hassen Aydi Samina Batul Amna Naz Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications Journal of Function Spaces |
| title | Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications |
| title_full | Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications |
| title_fullStr | Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications |
| title_full_unstemmed | Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications |
| title_short | Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications |
| title_sort | coincidence point results on relation theoretic fw rg contractions and applications |
| url | http://dx.doi.org/10.1155/2021/9937318 |
| work_keys_str_mv | AT muhammadaslam coincidencepointresultsonrelationtheoreticfwrgcontractionsandapplications AT hassenaydi coincidencepointresultsonrelationtheoreticfwrgcontractionsandapplications AT saminabatul coincidencepointresultsonrelationtheoreticfwrgcontractionsandapplications AT amnanaz coincidencepointresultsonrelationtheoreticfwrgcontractionsandapplications |