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Volume 2, Issue 2, Article 23 |
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Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions
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Authors: |
Gejun Bao, Yi Ling, Hari M. Srivastava, |
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Keywords:
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Distortion inequalities, analytic functions, fractional derivatives, univalent functions, convex functions, hypergeometric function |
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Date Received:
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16/10/00 |
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Date Published:
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04/03/00 |
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Subject Codes: |
30C45,26A33,33C05
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Editors: |
Pietro Cerone, |
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Abstract: |
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.
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