B. Sudharsanan - Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College (Autonomous), Chennai, 600106, Tamilnadu, India. S. Gunasekar - PG and Research Department of Mathematics, Pachaiyappa's College, Chennai- 600030, Tamilnadu, India. T. G. Shaba - Department of Mathematics and Statistics, Redeemer's University, Ede 232101, Amman, Nigeria. L. Ragoub - Mathematics Department, University of Prince Mugrin, P.O. Box 41040, Al Madinah 42241, Saudi Arabia. D. Breaz - Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania. L.-I. Cotîrla - Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania.
This study explores a novel category of bi-univalent functions within the open unit disk, defined through subordination principles and linked to Jacobi polynomials. By utilizing the structural properties of these classical orthogonal polynomials, we derive sharp bounds for the initial Taylor-Maclaurin coefficients, specifically \(\left| \tau_2 \right|\) and \(\left| \tau_3 \right|\), for functions within this subclass. Furthermore, we establish a Fekete-Szeg\"{o} type inequality involving the functional \(\left| \tau_3 - \varrho \tau_2^2 \right|\), where \(\varrho\) is a real parameter. The results obtained generalize and extend various known results in the context of bi-univalent function theory. Notably, this framework has potential applications in image enhancement, where the derived function classes contribute to improved edge detection, feature preservation, and contrast adjustment. Incorporating Jacobi polynomials enhances the theoretical framework while showcasing the method's strength and versatility in processing and improving various image types.
B. Sudharsanan, S. Gunasekar, T. G. Shaba, L. Ragoub, D. Breaz, L.-I. Cotîrla, Jacobi polynomials on a novel subclass of bi-univalent functions for advanced image processing applications, Journal of Mathematics and Computer Science, 41 (2026), no. 3, 322--333
Sudharsanan B., Gunasekar S., Shaba T. G., Ragoub L., Breaz D., Cotîrla L.-I., Jacobi polynomials on a novel subclass of bi-univalent functions for advanced image processing applications. J Math Comput SCI-JM. (2026); 41(3):322--333
Sudharsanan, B., Gunasekar, S., Shaba, T. G., Ragoub, L., Breaz, D., Cotîrla, L.-I.. "Jacobi polynomials on a novel subclass of bi-univalent functions for advanced image processing applications." Journal of Mathematics and Computer Science, 41, no. 3 (2026): 322--333
