A Comprehensive Study on Advancement in Hybrid Contraction and Graphical Analysis of £ -Fuzzy Fixed Points with Application

Maliha Rashid, Akbar Azam, Fatima Dar, Faryad Ali () and Mohammed A. Al-Kadhi
Additional contact information
Maliha Rashid: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Akbar Azam: Department of Mathematics, Grand Asian University, Sialkot 51310, Pakistan
Fatima Dar: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Faryad Ali: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia
Mohammed A. Al-Kadhi: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia

Mathematics, 2023, vol. 11, issue 21, 1-25

Abstract: 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 Z -contraction in the perspective of £ -fuzzy set-valued maps for extended ♭-metric spaces. Sufficient criteria for obtaining £ -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 £ -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.

Keywords: extended ?-metric space; metric space equipped with a graph; £-fuzzy set-valued map; £-fuzzy fixed point; hybrid contraction; simulation function; Z -contraction; graphic contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/21/4489/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/21/4489/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:21:p:4489-:d:1270769

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().