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RESEARCH ARTICLE

Fixed point results for generalized rectangular fuzzy b-metric-like spaces and applications

Umar Ishtiaq1* ,  Fahad Jahangeer2 ,  Iqra Shereen2 ,  Tayyab Kamran3,4 ,  Ioan-Lucian Popa5,6
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1 Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore, Punjab, Pakistan
2 Department of Mathematics, Faculty of Natural Sciences, Quaid-i-Azam University, Islamabad, Punjab, Pakistan
3 Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku, Azerbaijan
4 Jadara Research Center, Jadara University, Irbid, Jordan
5 Department of Informatics, Mathematics, and Electronics, Faculty of Informatics and Engineering, 1 Decembrie 1918 University of Alba Iulia, Alba Iulia, Transylvania, Romania
6 Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, Transilvania, Romania
IJOCTA, 025420179 https://doi.org/10.36922/IJOCTA025420179
Received: 14 October 2025 | Revised: 9 November 2025 | Accepted: 11 November 2025 | Published online: 27 March 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper introduces a new extended rectangular fuzzy b-metric-like space that generalizes the existing frameworks of the extended rectangular and fuzzy b-metric spaces. Within this setting, we establish several fixed-point theorems for Ciric-type and Banach-type contractions, accompanied by a series of corollaries, propositions, and conditions that further illustrate the proposed concept. These results unify and extend many known theorems in fuzzy metric theory. Moreover, we provided several non-trivial examples to validate of the main results. A flow diagram was provided to demonstrate the generalized structure. Additionally, we applied the fuzzy integral equation to establish the uniqueness and existence of our main result.

Graphical abstract
Keywords
Fixed point
Operator equations
Hölderian
Nonlinear functional
Lipschitzian
Integral equations
Funding
None.
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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