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On \(k\)-uniformly close-to-convex functions of complex order. (English) Zbl 1176.30050

Summary: We define and study some subclasses of analytic functions by using a fractional derivative operator. Some interesting properties, coefficients problems, and inclusion results of these classes are investigated. It is also shown that these classes are closed under convolution with convex functions, and some applications are given.

MSC:

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