WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
Applications of Borel Distribution for a New Family
of Bi-Univalent Functions Defined by Horadam
Polynomials
Authors: S. R. Swamy, Alina Alb Lupaş, Abbas Kareem Wanas, J. Nirmala
Abstract: In this paper, by making use of Borel distribution we introduce a new family GΣ(δ, γ, λ, τ, r) of normalized analytic and bi-univalent functions in the open unit disk U, which are associated with Horadam polynomials. We establish upper bounds for the initial Taylor-Maclaurin coefficients |a2| and |a3| of functions belonging to the analytic and bi-univalent function family which we have introduced here. Furthermore, we establish the Fekete-Szeg¨o problem of functions in this new family.
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Keywords: Bi-univalent function, Bazilevič function, λ-Pseudo-starlike function, Borel distribution, Horadam polynomials, Upper bounds, Fekete-Szego problem.
Pages: 630-636
DOI: 10.37394/23206.2021.20.67
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 20, 2021, Art. #67