Extending F-Contraction Theory: Fixed Points in Triple-Controlled S-Metric Spaces

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6847

Keywords:

Fixed point, , Triple Controlled $S$-metric type spaces, $(\alpha _{s}, \mu _{s}, (Q,h)-\mathcal{F})-$contraction, $S$-metric spaces, pair $% (Q, h)$ upper class

Abstract

This paper explores the landscape of fixed point theory by introducing two novel classes of contraction mappings: the (αs, νs,(Q, h)-F)-contraction and the (αs, ηs, νs,(Q, h)-F)-contraction, defined within the rich structure of triple-controlled S-metric type spaces. These mappings are constructed using a blend of αs- and ηs-admissibility, νs-subadmissibility, and a pair of upper-class functions (Q, h), integrated with Wardowski’s powerful F-contraction approach. Our results significantly extend the classical (αs F)-contraction framework by proving the existence and uniqueness of fixed points under these generalized settings. Furthermore, we derive meaningful corollaries by specifying various (Q, h) pairs, illustrating the versatility and depth of the proposed theory and its contribution to the advancement of fixed point results in generalized metric environments.

Author Biography

  • Fatima M. Azmi, Department of Mathematics and Sciences, Prince Sultan University. Riyadh 11586, Saudi Arabia.

    Professor of Mathematics. She received Ph.D. degrees in Mathematics from the University of Colorado, Boulder, CO. USA. She has over 20 years of teaching and research experience in the field of Mathematics. Her current research interest includes Fixed point theorem on metric type spaces, Mathematics Education, Education and Technology, C*-algebras, Fréchet*-algebras, and Noncommutative Geometry.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Fatima M. Azmi, Arsalan Hojjat Ansari, Seyyed Hossein Jafari Petroudi

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How to Cite

Extending F-Contraction Theory: Fixed Points in Triple-Controlled S-Metric Spaces. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6847. https://doi.org/10.29020/nybg.ejpam.v18i4.6847