On a subclass of the analytic and bi-univalent functions satisfying subordinate condition defined by $q$-derivativ

Authors: NİZAMİ MUSTAFA, SEMRA KORKMAZ

Abstract: In this paper, we introduce and examine certain subclass $\ M_{q,\Sigma }\left( \varphi ,\beta \right) $ of analytic and bi-univalent functions on the open unit disk in the complex plane. Here, we give coefficient bound estimates, upper bound estimate for the second Hankel determinant and Fekete-Szegö inequality for the function belonging to this class. Some interesting special cases of the results obtained here are also discussed.

Keywords: Subordination, convex function, quasi close-to-$q$-convex function, $q$-derivative

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