Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a <i>q</i>-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients <inline-formula> <math display="inline"> <se...

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Bibliographic Details
Main Authors: Sheza M. El-Deeb, Teodor Bulboacă, Bassant M. El-Matary
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Mathematics
Subjects:
bi-univalent functions
hadamard (convolution) product
coefficients bounds
<i>q</i>-derivative operator
differential subordination
Online Access:https://www.mdpi.com/2227-7390/8/3/418
Description
Summary:In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a <i>q</i>-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>2</mn> </msub> </mfenced> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>3</mn> </msub> </mfenced> </semantics> </math> </inline-formula> for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.
ISSN:2227-7390

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