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Applications of fractional calculus to parabolic starlike and uniformly convex functions

✍ Scribed by H.M. Srivastava; A.K. Mishra

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
566 KB
Volume
39
Category
Article
ISSN
0898-1221

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✦ Synopsis

Let A be the class of analytic functions in the open unit disk U. Given 0 ~ A < 1, let ~x be the operator defined on ,4 by

where D~I is the fractional derivative of f of order A. A function f in ,4 is said to be in the class SPx if ~Af is a parabolic starlike function. In this paper, several basic properties and characteristics of the class SPA are investigated. These include subordination, inclusion, and growth theorems, clarapreserving operators, Fekete-Szeg6 problems, and sharp estimates for the first few coefficients of the inverse function.

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