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Wongsaijai, Ben; Sukantamala, Nattakorn

Certain properties of some families of generalized starlike functions with respect to \(q\)-calculus. (English) Zbl 1470.30019

Abstr. Appl. Anal. 2016, Article ID 6180140, 8 p. (2016).
Summary: By making use of the concept of \(q\)-calculus, various types of generalized starlike functions of order \(\alpha\) were introduced and studied from different viewpoints. In this paper, we investigate the relation between various former types of \(q\)-starlike functions of order \(\alpha\). We also introduce and study a new subclass of \(q\)-starlike functions of order \(\alpha\). Moreover, we give some properties of those \(q\)-starlike functions with negative coefficient including the radius of univalency and starlikeness. Some illustrative examples are provided to verify the theoretical results in case of negative coefficient functions class.

Cited in 14 Documents

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C55 General theory of univalent and multivalent functions of one complex variable
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