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Open AccessArticle

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
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Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 36155-316, Shahrood 36155-316, Iran
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 172; https://doi.org/10.3390/math8020172
Received: 29 December 2019 / Revised: 20 January 2020 / Accepted: 20 January 2020 / Published: 1 February 2020
(This article belongs to the Special Issue Complex Analysis and Its Applications 2019)
In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results. View Full-Text
Keywords: analytic functions; univalent functions; bi-univalent functions; coefficient estimates; Taylor-Maclaurin coefficients; Faber polynomial expansion; differential subordination; Tremblay fractional derivative operator analytic functions; univalent functions; bi-univalent functions; coefficient estimates; Taylor-Maclaurin coefficients; Faber polynomial expansion; differential subordination; Tremblay fractional derivative operator
MDPI and ACS Style

Srivastava, H.M.; Motamednezhad, A.; Adegani, E.A. Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator. Mathematics 2020, 8, 172.

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