Publication: Distortion estimate and radius of starlikeness for generalized p-valent close-to-star functions
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Date
2013
Authors
Özkan, H. Esra
Yavuz Duman, Emel
Journal Title
Journal ISSN
Volume Title
Publisher
HIKARI
Abstract
Let A(p, n), n ≥ 1, p ≥ 1 be the class of all analytic functions in the
open unit disc D = {z| |z| < 1} of the form f(z) = zp + anp+1znp+1 +
anp+2znp+2 + ··· . Let g(z) be an element of A(p, n) such that g(z)
satisfies the condition Re
z g
(z)
g(z)
> 0 for all z ∈ D, we then call g(z) the
generalized p−valent starlike function in D. The class of such functions
is denoted by S∗(p, n). Let s(z) be an element of A(p, n) and g(z) be an
element of S∗(p, n). If the condition Re s(z)
g(z)
> 0 (z ∈ D), is satisfied
then s(z) is called the generalized p−valent close-to-star function in D.
The class of such functions is denoted by S∗K(p, n).
The aim of this paper is to give a distortion estimation and the
radius of starlikeness of the class S∗K(p, n).
Description
Keywords
Close-to-star function, the radius of starlikeness, distortion estimate