Efficient low-light image enhancement via balancing polynomials-based adaptive contrast control using coefficient inequalities of a subclass of bi-univalent functions

Vanithakumari Balasubramaniam; Sibel Yalçin; Saravanan Gunasekar; Selvaraj Palanisamy; Vanithakumari Balasubramaniam; Sibel Yalçin; Saravanan Gunasekar; Selvaraj Palanisamy

doi:10.3934/math.20261273

AIMS Mathematics

2026, Volume 11, Issue 10: 32394-32408. doi: 10.3934/math.20261273

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Efficient low-light image enhancement via balancing polynomials-based adaptive contrast control using coefficient inequalities of a subclass of bi-univalent functions

1.
Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Chennai 601103, Tamil Nadu, India; vanithagft@gmail.com (VB); selvamath89@gmail.com (SP)
2.
Department of Mathematics, Bursa Uludag University, Bursa 16059, Turkey; syalcin@uludag.edu.tr (SY)
3.
PG and Research Department of Mathematics, Pachaiyappa's College, Chennai 600030, India; gsaran825@yahoo.com (SG)

Received: 19 June 2026 Revised: 16 August 2026 Accepted: 03 September 2026 Published: 08 October 2026
MSC : Primary 30C45; Secondary 30C50, 33C45

In this research work, we introduced a novel subclass of bi-univalent functions associated with balancing polynomials. For this class, we derived coefficient estimates $ |\alpha_{2}| $, $ |\alpha_{3}| $ along with Fekete–Szegö inequalities. Motivated by these theoretical findings, we proposed a new model based on balancing polynomials. The proposed low-light enhancement model consists of gamma correction and adaptive polynomial components, which make the image brighter without losing details. To avoid over-enhancement, a control mechanism based on the contrast improvement index (CII) was adopted to ensure that the performance is the same in different lighting situations. According to tests on a number of low-light images, the proposed method had higher entropy with controlled contrast than other traditional methods. By maintaining a consistent balance between detail enhancement and natural visual appearance, the technique validated its effectiveness and appropriateness for practical image-enhancement applications.
- bi-univalent functions,
- balancing polynomials,
- Fekete–Szegöinequalities,
- low-light enhancement,
- gamma correction,
- entropy,
- contrast improvement index (CII)
Citation: Vanithakumari Balasubramaniam, Sibel Yalçin, Saravanan Gunasekar, Selvaraj Palanisamy. Efficient low-light image enhancement via balancing polynomials-based adaptive contrast control using coefficient inequalities of a subclass of bi-univalent functions[J]. AIMS Mathematics, 2026, 11(10): 32394-32408. doi: 10.3934/math.20261273

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Abstract

In this research work, we introduced a novel subclass of bi-univalent functions associated with balancing polynomials. For this class, we derived coefficient estimates $ |\alpha_{2}| $, $ |\alpha_{3}| $ along with Fekete–Szegö inequalities. Motivated by these theoretical findings, we proposed a new model based on balancing polynomials. The proposed low-light enhancement model consists of gamma correction and adaptive polynomial components, which make the image brighter without losing details. To avoid over-enhancement, a control mechanism based on the contrast improvement index (CII) was adopted to ensure that the performance is the same in different lighting situations. According to tests on a number of low-light images, the proposed method had higher entropy with controlled contrast than other traditional methods. By maintaining a consistent balance between detail enhancement and natural visual appearance, the technique validated its effectiveness and appropriateness for practical image-enhancement applications.

References

[1]	B. Aarthy, B. S. Keerthi, Enhancement of various images using coefficients obtained from a class of Sakaguchi type functions, Sci. Rep., 13 (2023), 18722. https://doi.org/10.1038/s41598-023-45938-y doi: 10.1038/s41598-023-45938-y
[2]	A. Amourah, A. Alamoush, M. Al-Kaseasbeh, Gegenbauer polynomials and bi-univalent functions, Palest. J. Math., 10 (2021), 625–632.
[3]	A. Behera, G. K. Panda, On the square roots of triangular numbers, Fibonacci Quart., 37 (1999), 98–105. https://doi.org/10.1080/00150517.1999.12428864 doi: 10.1080/00150517.1999.12428864
[4]	D. A. Brannan, J. G. Clunie, Aspects of contemporary complex analysis, London: Academic Press, 1980.
[5]	R. K. Davala, G. K. Panda, On sum and ratio formulas for balancing numbers, J. Ind. Math. Soc., 82 (2015), 23–32.
[6]	X. Dong, Y. Pang, J. Wen, Fast efficient algorithm for enhancement of low lighting video, ACM SIGGRAPH Posters, 2010, 1. https://doi.org/10.1145/1836845.1836920 doi: 10.1145/1836845.1836920
[7]	R. Frontczak, A note on hybrid convolutions involving balancing and Lucas-balancing numbers, Appl. Math. Sci., 12 (2018), 1201–1208. https://doi.org/10.12988/ams.2018.87111 doi: 10.12988/ams.2018.87111
[8]	R. Frontczak, Sums of balancing and Lucas-balancing numbers with binomial coefficients, Int. J. Math. Anal., 12 (2018), 585–594. https://doi.org/10.12988/ijma.2018.81067 doi: 10.12988/ijma.2018.81067
[9]	J. R. Jebacass, P. Balasubramaniam, Low light enhancement algorithm for color images using intuitionistic fuzzy sets with histogram equalization, Multimed. Tools Appl., 81 (2022), 8093–8106. https://doi.org/10.1007/s11042-022-12087-9 doi: 10.1007/s11042-022-12087-9
[10]	G. Jiang, S. C. F. Lin, C. Y. Wong, M. A. Rahman, T. R. Ren, N. Kwok, et al., Color image enhancement with brightness preservation using a histogram specification approach, Optik, 126 (2015), 5656–5664. https://doi.org/10.1016/j.ijleo.2015.08.173 doi: 10.1016/j.ijleo.2015.08.173
[11]	B. Khan, M. G. Khan, T. G. Shaba, Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution, J. Nonlinear Sci. Appl., 16 (2023), 180–197. https://doi.org/10.22436/jnsa.016.03.04 doi: 10.22436/jnsa.016.03.04
[12]	M. Lewin, On a coefficient problem for bi-univalent functions, P. Am. Math. Soc., 18 (1967), 63–68. https://doi.org/10.2307/2035225 doi: 10.2307/2035225
[13]	P. Muthukumar, N. R. Babu, P. Balasubramaniam, Detecting critical point of fractional-order chemical system with synchronization and application to image enhancement technique, P. Natl. A. Sci. India A, 91 (2021), 661–674. https://doi.org/10.1007/s40010-021-00763-8 doi: 10.1007/s40010-021-00763-8
[14]	E. K. Nithiyanandham, B. S. Keerthi, A new proposed model for image enhancement obtained from a class of Sakaguchi-type function, Signal Image Video P., 18 (2024), 1455–1462. https://doi.org/10.1007/s11760-023-02861-z doi: 10.1007/s11760-023-02861-z
[15]	G. Saravanan, S. Baskaran, B. Vanithakumari, L. Alnaji, T. G. Shaba, I. Al-Shbeil, et al., Bernoulli polynomials for a new subclass of Te-univalent functions, Heliyon, 10 (2024), e33953. https://doi.org/10.1016/j.heliyon.2024.e33953 doi: 10.1016/j.heliyon.2024.e33953
[16]	G. Saravanan, B. Sudharsanan, B. Vanithakumari, S. Altınkaya, Bi-univalent characteristics for a particular class of Bazilevič functions generated by convolution using Balancing polynomials, Jordan J. Math. Stat., 18 (2025), 381–392. Available from: https://jjms.yu.edu.jo/index.php/jjms/article/view/1417.
[17]	G. Saravanan, S. Baskaran, B. Vanithakumari, S. Bulut, Sakaguchi type functions defined by balancing polynomials, Math. Bohem., 150 (2025), 71–83. http://dx.doi.org/10.21136/MB.2024.0173-23 doi: 10.21136/MB.2024.0173-23
[18]	K. S. Sundari, B. S. Keerthi, Enhancing low-light images using Sakaguchi type function and Gegenbauer polynomial, Sci. Rep., 14 (2024), 29679. https://doi.org/10.1038/s41598-024-80605-w doi: 10.1038/s41598-024-80605-w
[19]	B. Vanithakumari, G. Saravanan, B. Sudharsanan, S. Yalçın, Horadam polynomials for a new subclass of Sakaguchi-type bi-univalent functions defined by $(p, q)$-derivative operator, Commun. Korean Math. S., 39 (2024), 461–470.
[20]	S. Yalçın, K. Muthunagai, G. Saravanan, A subclass with bi-univalence involving $(p, q)$-Lucas polynomials and its coefficient bounds, Bol. Soc. Mat. Mex., 26 (2020), 1015–1022. https://doi.org/10.1007/s40590-020-00294-z doi: 10.1007/s40590-020-00294-z

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