On extremal problems related to integral transforms of a class of analytic functions

Balasubramanian, R. ; Ponnusamy, S. ; Prabhakaran, D. J. (2007) On extremal problems related to integral transforms of a class of analytic functions Journal of Mathematical Analysis and Applications, 336 (1). pp. 542-555. ISSN 0022-247X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00222...

Related URL: http://dx.doi.org/10.1016/j.jmaa.2007.02.076

Abstract

For γ ≥ 0 and β<1 given, let Pγ (β) denote the class of all analytic functions f in the unit disk with the normalization f(0)=f'(0)−1=0 and satisfying the condition Re{e(f'(z) +γzf"(z) − β)} > 0, z ε D, for some φ ∈ R. We shall investigate the integral transform Vλ(f)(z) = ∫01 λ(t) f(tz)/t dt, where λ is a nonnegative real valued function normalized by ∫01λ(t)dt = 1. From our main results we get conditions on the number β and the function λ such that Vλ(f) is starlike of order μ (0≤μ≤½ ) when f ∈ Pγ(β). As applications we study various choices of λ(t), related to classical integral transforms.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Hadamard Product; Analytic; Univalent; Starlike and Convex Functions
ID Code:1285
Deposited On:04 Oct 2010 07:55
Last Modified:16 May 2011 04:25

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