Applications of duality principle to integral transforms of analytic functions

Balasubramanian, R. ; Ponnusamy, S. (1999) Applications of duality principle to integral transforms of analytic functions Complex Variables and Elliptic Equations, 38 (4). pp. 289-305. ISSN 0278-1077

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Related URL: http://dx.doi.org/10.1080/17476939908815171

Abstract

Let A be the class of functions analytic in the unit disk and normalized by f(0)=f'(0)+1=0 Let S, S(y), and K(y) be respectively the classes of normalized univalent functions, starlike functions of order y and convex functions of order y. In this paper we investigate the properties of the integral transform Vλ(f) = ∫01 λ(t) f(tz)/t dt, f ∈ A where λ is a non-negative real valued function normalized by ∫01 λ(t)dt=1. From our main results we get conditions on λ and the class Fso that Vλ(f) maps F into various subclasses of the class of univalent functions. As a corollary to our results, we give an affirmative answer in support of a conjecture of Kim: f is a member of S or S(y) or K(y), then the function φ(3,3+ αz) f(z) belongs to the same class for α>1, where φ(b,c;z) f(z) stands for the convolution of incomplete beta function with f∈A.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Ltd.
Keywords:Integral Transforms; Incomplete Beta Function; Convex; Starlike and Univalent Functions
ID Code:1349
Deposited On:05 Oct 2010 12:43
Last Modified:16 May 2011 04:38

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