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Fekete-Szego estimates and second Hankel determinant for a generalized subfamily of analytic functions defined by \(q\)-differential operator. (English) Zbl 1470.30011

Summary: In this paper, we considered a family of analytic and univalent functions having positive real parts in the unit disk and defined by a \(q\)-difference operator. The coefficients, the Fekete-Szegö estimates and the second Hankel determinant were established for the family of functions. Our family of functions generalized some earlier known ones and by varying some parameters, our results also generalized some known ones.

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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