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On unified subclass of complex order connected with \(q\) confluent hypergeometric distribution. (English) Zbl 1486.30033

Summary: In this paper, we apply the concept of \(q\)-confluent hypergeometric distribution to introduce and study a unified subclass of univalent functions of complex order \(B^{\lambda,q}_{\zeta,\gamma} (\Upsilon;b,c,m)\) consisting of all analytic functions, and some known consequences of the results are also derived for this class.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
11B65 Binomial coefficients; factorials; \(q\)-identities
47B38 Linear operators on function spaces (general)
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