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Geometric properties for a family of holomorphic functions associated with Wanas operator defined on complex Hilbert space. (English) Zbl 1482.30052

Summary: By making use of Wanas operator, we aim to introduce and investigate a certain family of univalent holomorphic functions with negative coefficients defined on complex Hilbert space. We present some important geometric properties of this family such as coefficient estimates, convexity, distortion and growth, radii of starlikeness and convexity. We also discuss the extreme points for functions belonging to this family.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
32K12 Holomorphic maps with infinite-dimensional arguments or values
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