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

• 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

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.