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Research Article | Open Access

New developments in fixed point theorems for θ-Branciari contractions on strong-controlled Branciari b distance spaces

Dania Santina1,2( ), Wan Ainun Mior Othman2( ), Kok Bin Wong2, Nabil Mlaiki1
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Institute of Mathematical Sciences, Faculty of Science, University Malaya, Kuala Lumpur, Malaysia
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Abstract

In this paper, we introduced the strong-controlled Branciari b-distance, a generalized metric structure designed to consolidate disparate fixed point theorems scattered throughout existing literature. Through illustrative examples, we demonstrated how this framework subsumes and extends previous results. We further established the applicability of our theoretical developments by presenting a concrete problem whose solution leverages the properties of strong-controlled Branciari b-distance spaces.

Keywords

metric space (Msp)Branciari distance (Bd)strong-controlled Branciari b-distance (SCBbd)θ-Branciari contraction (θBC)Ciric-Reich-Rus-type θ-Branciari contraction (CRRT − θBC)
CLC number: 47H10, 54H25

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 28100-28114
DOI: 10.3934/math.20251235

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Cite this article:
Santina D, Othman WAM, Wong KB, et al. New developments in fixed point theorems for θ-Branciari contractions on strong-controlled Branciari b distance spaces. AIMS Mathematics, 2025, 10(12): 28100-28114. https://doi.org/10.3934/math.20251235

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Received: 05 August 2025
Revised: 16 November 2025
Accepted: 24 November 2025
Published: 01 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)