ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. 69, 1 (2000)
pp. 1-8
CHARACTERIZATION PROPERTIES FOR STARLIKENESS AND CONVEXITY OF SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A CLASS OF FRACTIONAL DERIVATIVE OPERATORS
R. K. RAINA and T. S. NAHAR
Abstract.
This paper investigates the characterization properties exhibited by a class of fractional derivative operators of certain analytic functions in the open unit disk to be starlike or convex. Further characterization theorems associated with the Hadamard product (or convolution) are also studied.
AMS subject classification.
26A33, 30C45
Keywords.
Starlike functions, convex functions, fractional derivative operators, Hadamard product
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