A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application
Hybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy <inline-formula><math xmlns="http://www.w3.org/1998/Math/...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4489 |
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| author | Maliha Rashid Akbar Azam Fatima Dar Faryad Ali Mohammed A. Al-Kadhi |
| author_facet | Maliha Rashid Akbar Azam Fatima Dar Faryad Ali Mohammed A. Al-Kadhi |
| author_sort | Maliha Rashid |
| collection | DOAJ |
| description | Hybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">Z</mi></semantics></math></inline-formula>-contraction in the perspective of <i>£</i>-fuzzy set-valued maps for extended ♭-metric spaces. Sufficient criteria for obtaining <i>£</i>-fuzzy fixed points for this contraction have been established. In addition, the hypotheses of its main result are endorsed by some nontrivial supportive examples featuring graphical illustrations. Consequently, the concept of graphical extended ♭-metric spaces is introduced and a <i>£</i>-fuzzy fixed point result in the context of newly defined space is derived. Illustrative examples, incorporating relevant graphs, are provided with the support of a computer simulation to validate the established results, enhancing the understanding of the underlying notions and investigations. The concepts presented here not only considerably improve, enrich, and extend a number of well-known pre-existing fixed-point results but also assemble and merge several ones in the corresponding domain. |
| first_indexed | 2024-03-11T11:25:37Z |
| format | Article |
| id | doaj.art-afeb46204a9f4b6c8d58b54163e6b803 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:37Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-afeb46204a9f4b6c8d58b54163e6b8032023-11-10T15:08:03ZengMDPI AGMathematics2227-73902023-10-011121448910.3390/math11214489A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with ApplicationMaliha Rashid0Akbar Azam1Fatima Dar2Faryad Ali3Mohammed A. Al-Kadhi4Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics, Grand Asian University, Sialkot 51310, PakistanDepartment of Mathematics and Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi ArabiaHybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">Z</mi></semantics></math></inline-formula>-contraction in the perspective of <i>£</i>-fuzzy set-valued maps for extended ♭-metric spaces. Sufficient criteria for obtaining <i>£</i>-fuzzy fixed points for this contraction have been established. In addition, the hypotheses of its main result are endorsed by some nontrivial supportive examples featuring graphical illustrations. Consequently, the concept of graphical extended ♭-metric spaces is introduced and a <i>£</i>-fuzzy fixed point result in the context of newly defined space is derived. Illustrative examples, incorporating relevant graphs, are provided with the support of a computer simulation to validate the established results, enhancing the understanding of the underlying notions and investigations. The concepts presented here not only considerably improve, enrich, and extend a number of well-known pre-existing fixed-point results but also assemble and merge several ones in the corresponding domain.https://www.mdpi.com/2227-7390/11/21/4489extended ♭-metric spacemetric space equipped with a graph£-fuzzy set-valued map£-fuzzy fixed pointhybrid contractionsimulation function |
| spellingShingle | Maliha Rashid Akbar Azam Fatima Dar Faryad Ali Mohammed A. Al-Kadhi A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application Mathematics extended ♭-metric space metric space equipped with a graph £-fuzzy set-valued map £-fuzzy fixed point hybrid contraction simulation function |
| title | A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application |
| title_full | A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application |
| title_fullStr | A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application |
| title_full_unstemmed | A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application |
| title_short | A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of <i>£</i>-Fuzzy Fixed Points with Application |
| title_sort | comprehensive study on advancement in hybrid contraction and graphical analysis of i £ i fuzzy fixed points with application |
| topic | extended ♭-metric space metric space equipped with a graph £-fuzzy set-valued map £-fuzzy fixed point hybrid contraction simulation function |
| url | https://www.mdpi.com/2227-7390/11/21/4489 |
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