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Zbl 0993.30010
Srivastava, H.M.; Ling, Yi; Bao, Gejun
Some distortion inequalities associated with the fractional derivatives of analytic and univalent functions. (English)
[J] JIPAM, J. Inequal. Pure Appl. Math. 2, No.2, Paper No.23, 6 p. (2001). ISSN 1443-5756/e

Summary: For the classes $S$ and $K$ of (normalized) univalent and convex analytic functions, respectively, a number of authors conjectured interesting extensions of certain known distortion inequalities in terms of a fractional derivative operator. While examining and investigating the validity of these conjectures, many subsequent works considered various generalizations of the distortion inequalities relevant to each of these conjectures. The main object of this paper is to give a direct proof of one of the known facts that these conjectures are false. Several further distortion inequalities involving fractional derivatives are also presented.
[T.S.Nahar (Bhilwara)]

MSC 2000:: *30C45 Special classes of univalent and multivalent functions
26A33 Fractional derivatives and integrals (real functions)
33C05 Classical hypergeometric functions

Keywords: distortion inequalities; analytic functions; fractional derivatives; univalent functions; convex functions; hypergeometric function

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