Abstract
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.
Highlights
We recall the well-established fact that every function f ∈ S possesses its inverse f −1, which is defined by f −1 f ( z ) = z (z ∈ U)
We give several remarks and observations which related to the developments resented in this paper
| an | (n = 3) for subclass defined by Ali et al [47] (Theorem 2.1), which are not obtained until now
Summary
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan Received: 29 December 2019; Accepted: 20 January 2020; Published: 1 February 2020
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