Fixed Point Theorems in Fuzzy Metric Spaces via Generalized Graphic Rational \(\Theta\)-Contractions

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DOI: https://doi.org/10.28924/2291-8639-24-2026-342
Published: Oct 15, 2026
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Sidite Duraj, R. Pichailakshmi, Kastriot Zoto, E. Madhavi, K. Dinesh, Fixed Point Theorems in Fuzzy Metric Spaces via Generalized Graphic Rational \(\Theta\)-Contractions, Int. J. Anal. Appl., 24 (2026), 342.

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Sidite Duraj, R. Pichailakshmi, Kastriot Zoto, E. Madhavi, K. Dinesh

Abstract

The aim of this paper is to investigate fixed point results for a new class of graphic rational \(\Theta\)-contractions in complete fuzzy metric spaces endowed with a directed graph. By combining the graph-theoretic framework with rational contractive conditions involving \(\Theta\)-functions, several existence and uniqueness theorems are established. The obtained results generalize and unify various well-known contraction principles in the literature, including Banach-type, Hardy–Rogers-type, Čirić-type and integral-type contractions. The graph structure enables the treatment of mappings satisfying contractive conditions only on admissible pairs of points connected through graph edges. Sufficient conditions ensuring the convergence of Picard iterative sequences to unique fixed points are derived. A numerical example and convergence analysis are presented to illustrate the applicability of the theoretical findings. The established results extend several recent developments in fuzzy metric spaces and metric spaces endowed with graphs.

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