Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application
In this article, we introduce a relatively new concept of multi-valued <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>θ</mi> <mo>,</mo> <mi mathvariant="script">R</mi> <mo>)&...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/5/695 |
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| author | Md Hasanuzzaman Salvatore Sessa Mohammad Imdad Waleed M. Alfaqih |
| author_facet | Md Hasanuzzaman Salvatore Sessa Mohammad Imdad Waleed M. Alfaqih |
| author_sort | Md Hasanuzzaman |
| collection | DOAJ |
| description | In this article, we introduce a relatively new concept of multi-valued <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>θ</mi> <mo>,</mo> <mi mathvariant="script">R</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type. |
| first_indexed | 2024-03-10T20:05:22Z |
| format | Article |
| id | doaj.art-671164ae6d7946bab6a6ec79677d2320 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:05:22Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-671164ae6d7946bab6a6ec79677d23202023-11-19T23:18:38ZengMDPI AGMathematics2227-73902020-05-018569510.3390/math8050695Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an ApplicationMd Hasanuzzaman0Salvatore Sessa1Mohammad Imdad2Waleed M. Alfaqih3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, ItalyDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Hajjah University, Hajjah 1729, YemenIn this article, we introduce a relatively new concept of multi-valued <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>θ</mi> <mo>,</mo> <mi mathvariant="script">R</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.https://www.mdpi.com/2227-7390/8/5/695fixed pointmonotone type mappingsmulti-valued <i>θ</i>-contractionsbinary relationsintegral equations |
| spellingShingle | Md Hasanuzzaman Salvatore Sessa Mohammad Imdad Waleed M. Alfaqih Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application Mathematics fixed point monotone type mappings multi-valued <i>θ</i>-contractions binary relations integral equations |
| title | Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application |
| title_full | Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application |
| title_fullStr | Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application |
| title_full_unstemmed | Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application |
| title_short | Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application |
| title_sort | fixed point results for a selected class of multi valued mappings under i θ i i r i contractions with an application |
| topic | fixed point monotone type mappings multi-valued <i>θ</i>-contractions binary relations integral equations |
| url | https://www.mdpi.com/2227-7390/8/5/695 |
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