Computational Analysis of Unique Coupled Fixed Point Theorems in GFM-Spaces with an Application

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DOI: https://doi.org/10.28924/2291-8639-24-2026-305
Published: Oct 5, 2026
Cite as:
Saif Ur Rehman, Sovaiba Majeed, Sidra Akbar, Tayyab Mahmood, Ali Akgul, Dumitru Baleanu, Computational Analysis of Unique Coupled Fixed Point Theorems in GFM-Spaces with an Application, Int. J. Anal. Appl., 24 (2026), 305.

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Saif Ur Rehman, Sovaiba Majeed, Sidra Akbar, Tayyab Mahmood, Ali Akgul, Dumitru Baleanu

Abstract

In this paper, we establish some coupled fixed-point (FP) results in generalized fuzzy metric spaces (GFM-spaces) with a supportive three-dimensional column graph justification. We use the rectangular property of a GFM-space to prove the uniqueness of coupled FP findings in the said space under the coupled contraction conditions. In support of our findings, we provide illustrative, unique coupled FP numerical examples to validate our work. Further, we sketch a three-dimensional column graph using a numerical example to illustrate the inequality of coupled contraction in the aforementioned space. Moreover, we apply the Urysohn-type integral equations (UTIEs) to establish the existence and uniqueness of a coupled solution, thereby to unifying our work. Furthermore, we present an illustrative numerical example formulated in the setting of UTIEs which is not only verify the validity of our theoretical work but also establish the direct connection between the developed theory and its application, highlighting the reliability and effectiveness of the proposed approach.

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