Fixed point theorems for graphic $ \Theta $-contractions in $ \mathcal{F} $-metric spaces with applications to image processing

Maliha Rashid; Haseeba Bibi; Hadeel Z. Alzumi; Maliha Rashid; Haseeba Bibi; Hadeel Z. Alzumi

doi:10.3934/math.20251344

AIMS Mathematics

2025, Volume 10, Issue 12: 30639-30660. doi: 10.3934/math.20251344

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Research article

Fixed point theorems for graphic $ \Theta $-contractions in $ \mathcal{F} $-metric spaces with applications to image processing

1.
Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, Pakistan; maliha.rashid@iiu.edu.pk, haseeba_khan20@yahoo.com
2.
Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21493, Saudi Arabia; hzalzumi@uj.edu.sa

Received: 01 July 2025 Revised: 08 December 2025 Accepted: 23 December 2025 Published: 26 December 2025
MSC : 46S40, 47H10, 54H25

The aim of this research article is to introduce the notion of graphic $ \Theta $-contractions in the setting of $ \mathcal{F} $-metric spaces, and establish some novel fixed point results. To demonstrate the validity of our theoretical contributions, we include some illustrative examples. In addition, we extend our analysis by proving fixed point theorems for orbitally $ G $ continuous graphic $ \Theta $-contractions. A significant application of our results is the formulation of image denoising as a fixed point problem. Specifically, we define a contractive operator that refines pixel intensities through iterative updates based on the local neighborhood of each pixel. Using the principles of fixed point theory, we prove the existence and uniqueness of a stable denoised image that corresponds to the fixed point of the constructed mapping. Furthermore, we investigate the convergence properties of the iterative scheme under the assumptions of graphic $ \Theta $-contractions, thereby confirming its reliability and effectiveness.
- fixed point,
- $ \Theta $-contraction,
- $ \mathcal{F} $-metric space,
- graphs,
- self-mappings,
- image denoising
Citation: Maliha Rashid, Haseeba Bibi, Hadeel Z. Alzumi. Fixed point theorems for graphic $ \Theta $-contractions in $ \mathcal{F} $-metric spaces with applications to image processing[J]. AIMS Mathematics, 2025, 10(12): 30639-30660. doi: 10.3934/math.20251344

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Abstract

The aim of this research article is to introduce the notion of graphic $ \Theta $-contractions in the setting of $ \mathcal{F} $-metric spaces, and establish some novel fixed point results. To demonstrate the validity of our theoretical contributions, we include some illustrative examples. In addition, we extend our analysis by proving fixed point theorems for orbitally $ G $ continuous graphic $ \Theta $-contractions. A significant application of our results is the formulation of image denoising as a fixed point problem. Specifically, we define a contractive operator that refines pixel intensities through iterative updates based on the local neighborhood of each pixel. Using the principles of fixed point theory, we prove the existence and uniqueness of a stable denoised image that corresponds to the fixed point of the constructed mapping. Furthermore, we investigate the convergence properties of the iterative scheme under the assumptions of graphic $ \Theta $-contractions, thereby confirming its reliability and effectiveness.

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