On Subclasses Of Bi-Starlike Functions Defined By Tremblay Fractional Derivative Operator

Authors : Sevtap SÜMER EKER, Bilal ŞEKER

Pages : 226-232

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Publication Date : 2018-10-15

Article Type : Research Paper

Abstract :In this paper, we introduce and investigate new subclasses of strongly bi-starlike and bi-starlike functions defined by Tremblay fractional derivative operator in the open unit disk. Also we obtain upper bounds for the coefficients $|a_{2}|$ and $|a_{3}|$ of functions belonging to these classes. Unlike recent studies, we use different technique for obtain the upper bounds on the coefficients $|a_{3}|$. Theorems proved in this paper generalizes the results given in [3].
Keywords : bi starlike functions, Coefficient bounds and coefficient estimates, Fractional derivative, strongly bi starlike functions