On certain subclasses of bi-univalent functions associated with Jacobi polynomials and the Bell distribution with applications to image enhancement

Vanithakumari Balasubramaniam; Serkan Araci; Selvaraj Palanisamy; Vanithakumari Balasubramaniam; Serkan Araci; Selvaraj Palanisamy

doi:10.3934/math.20261265

AIMS Mathematics

2026, Volume 11, Issue 9: 32181-32198. doi: 10.3934/math.20261265

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Research article

On certain subclasses of bi-univalent functions associated with Jacobi polynomials and the Bell distribution with applications to image enhancement

1.
Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Chennai 601103, Tamil Nadu, India; vanithagft@gmail.com (V.B.); selvamath89@gmail.com (S.P.)
2.
Department of Computer Engineering, Faculty of Engineering, Hasan Kalyoncu University, TR-27010, Gaziantep, Türkiye; serkan.araci@hku.edu.tr (S.A.)

Received: 12 April 2026 Revised: 03 June 2026 Accepted: 23 June 2026 Published: 30 September 2026
MSC : 30C45

In this research work, we introduced a novel subclass $ \mathcal{B}_{\lambda}^{\vartheta, \varsigma}(\alpha, \beta; y, \zeta) $ of bi-univalent functions associated with the Bell distribution by using Jacobi polynomials. For this class, coefficient bounds $ |a_2| $ and $ |a_3| $, together with the corresponding Fekete–Szegö inequality were obtained. Based on these theoretical results, a simple and effective image enhancement algorithm (BJBIEA) model was proposed using a novel convolution strategy implemented through a $ 3 \times 3 $ mask. The outcomes showed that the suggested method for general-purpose image enhancement is effective, dependable, and adaptable. The extension of this framework to detail enhancement, edge extraction, and image resolution quality will be the focus of future work.
- bi-univalent functions,
- Fekete–Szegöproblem,
- Jacobi polynomials,
- Bell distribution,
- image enhancement,
- directional masks,
- convolution,
- Bell polynomials,
- Jacobi polynomials,
- grayscale image processing
Citation: Vanithakumari Balasubramaniam, Serkan Araci, Selvaraj Palanisamy. On certain subclasses of bi-univalent functions associated with Jacobi polynomials and the Bell distribution with applications to image enhancement[J]. AIMS Mathematics, 2026, 11(9): 32181-32198. doi: 10.3934/math.20261265

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Abstract

In this research work, we introduced a novel subclass $ \mathcal{B}_{\lambda}^{\vartheta, \varsigma}(\alpha, \beta; y, \zeta) $ of bi-univalent functions associated with the Bell distribution by using Jacobi polynomials. For this class, coefficient bounds $ |a_2| $ and $ |a_3| $, together with the corresponding Fekete–Szegö inequality were obtained. Based on these theoretical results, a simple and effective image enhancement algorithm (BJBIEA) model was proposed using a novel convolution strategy implemented through a $ 3 \times 3 $ mask. The outcomes showed that the suggested method for general-purpose image enhancement is effective, dependable, and adaptable. The extension of this framework to detail enhancement, edge extraction, and image resolution quality will be the focus of future work.

References

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