An application of the Mittag-Leffler-type Borel distribution and Gegenbauer polynomials on a certain subclass of bi-univalent functions

Abstract

The Mittag-Leffler-type Borel distribution is widely recognized and utilized as a beneficial and pertinent model across numerous applications. This study presents a new subclass of normalized analytic bi-univalent functions that combines Gegenbauer polynomials and the Mittag-Leffler-type Borel distribution. Employing this subclass enables us to derive novel approximations for Taylor-Maclaurin coefficients, |a2| and |a3|, as well as delve into the investigation of the Fekete-Szegö functional. Additionally, we explore a variety of new findings that arise through the specialization of parameters in our primary results.

Keywords

• Borel distribution
• Mittag-Leffler
• Gegenbauer polynomials
• Bi-univalent functions
• Analytic functions
• Fekete–Szegö problem