Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Ibtisam Aldawish, Tariq Al-Hawary and B. A. Frasin
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Ibtisam Aldawish: Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammed Ibn Saud Islamic University), P.O. Box 90950, Riyadh 11623, Saudi Arabia
Tariq Al-Hawary: Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
B. A. Frasin: Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq 25113, Jordan

Mathematics, 2020, vol. 8, issue 5, 1-11

Abstract: Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ? belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

Keywords: analytic functions; univalent functions; bi-univalent functions; Taylor–Maclaurin series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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