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Coefficient estimate of bi-Bazilevič functions associated with fractional \(q\)-calculus operators. (English) Zbl 1376.30010

Summary: In this paper, we introduce and investigate two new subclasses of the function class \(\Sigma\) of bi-univalent functions defined in the open unit disk, which are associated with fractional \(q\)-calculus operators, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\) for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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