Document Type : Research Paper


1 Department of Mathematical Science, Olusegun Agagu University of Science and Technology, Okiti Pupa, Ondo State, Nigeria.

2 Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, P.M.B. 4000, Ogbomoso, Oyo State, Nigeria.

3 Department of Mathematics, Faculty of Arts and Science, Istanbul Beykent University, 34500, Istanbul, Türkiye.


The present study is unique in exploring bi-univalent functions, which has recently garnered attention from many researchers in Geometric Function Theory (GFT). The uniqueness lies in utilizing a generalized discrete probability distribution and a zero-truncated Poisson distribution combined with generalized Gegenbauer polynomials featuring two variables. We aim to obtain coefficient bounds, the classical Fekete-Szegö inequality, and Hankel and Toeplitz determinants to generalize the probability of a gambler's ruin. Additionally, using the defined bi-univalent function classes contributes to the uniqueness of the obtained results.


Main Subjects

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