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Zbl 1207.30031
Srivastava, H.M.; Darus, Maslina; Ibrahim, Rabha W.
Classes of analytic functions with fractional powers defined by means of a certain linear operator. (English)
[J] Integral Transforms Spec. Funct. 22, No. 1-3, 17-28 (2011). ISSN 1065-2469; ISSN 1476-8291/e

Summary: Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator.

MSC 2000:: *30C45 Special classes of univalent and multivalent functions
30C50 Coefficient problems for univalent and multivalent functions
26A33 Fractional derivatives and integrals (real functions)

Keywords: Dziok-Srivastava operator; convex function; close-to-convex function; fractional integral operator

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