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A unified operator in fractional calculus and its applications to a nested class of analytic functions with negative coefficients. (English) Zbl 1019.30012

Summary: By making use of a fractional differintegral operator \(\Omega^\lambda_z (-\infty <\lambda<1)\), which unifies the concepts of fractional derivative and fractional integral, we introduce and study a nested class \({\mathcal T}_\lambda (\alpha)\) \((0\leq \alpha<1)\) of analytic functions with negative coefficients. Various growth and distortion theorems, and some general results pertaining to the Strohäcker-Marx problem, are obtained for the class \({\mathcal T}_\lambda (\alpha)\).

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
26A33 Fractional derivatives and integrals
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