International Journal of Nonlinear Analysis and Applications

Comprehensive subclass of univalent functions associated with the Gegenbauer polynomial and the Bahalola operator

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, P.O. Box: 19395-3697, Tehran, Iran

Abstract

Our objective in this paper is to introduce a newly constructed subclass of univalent functions. The Gegenbauer Polynomials are very successful in the theory of polynomials because they extend many polynomials, such as Legendre, Chebyshev polynomials, etc. Also, the Babolala operator for a fixed real number is used. Furthermore, by applying the convolution structures and subordination property, the new subclass is obtaind. For this new subclass, first, the share coefficient bounds are determined. These coefficient estimates are very important to obtain the geometric properties. So after that, we obtain the radii of starlikeness, convexity and close-to-convexity. Also, under some restrictions on parameters, we show that the newly defined subclass has a convolution-preserving property. Finally, the convexity of this subclass is pointed out. Our objective in this paper is to introduce a newly constructed subclass of univalent functions. The Gegenbauer Polynomials are very successful in the theory of polynomials because they extend many polynomials, such as Legendre, Chebyshev polynomials, etc. Also, the Babolala operator for a fixed real number is used. Furthermore, by applying the convolution structures and subordination property, the new subclass is obtaind. For this new subclass, first, the share coefficient bounds are determined. These coefficient estimates are very important to obtain the geometric properties. So after that, we obtain the radii of starlikeness, convexity and close-to-convexity. Also, under some restrictions on parameters, we show that the newly defined subclass has a convolution-preserving property. Finally, the convexity of this subclass is pointed out.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 20 November 2025
  • Receive Date: 22 October 2024
  • Revise Date: 08 February 2025
  • Accept Date: 30 July 2025