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Distortion inequalities for analytic and univalent functions associated with certain fractional calculus and other linear operators. (English) Zbl 0991.30007
Rassias, Themistocles M. (ed.) et al., Analytic and geometric inequalities and applications. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 478, 349-374 (1999).
Summary: By applying certain operators of fractional calculus (that is, fractional integral and fractional derivative), the author presents a systematic investigation of several generalizations of various growth-and-distortion type inequalities for some novel classes of analytic and univalent functions. These general inequalities are shown to stem naturally from some recent conjectures and theorems in geometric function theory.
##### MSC:
 30C45 Special classes of univalent and multivalent functions 26A33 Fractional derivatives and integrals (real functions) 33C20 Generalized hypergeometric series, ${}_{p}{F}_{q}$