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 P_{γ} (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^{iφ}(f'(z) +γzf"(z) − β)} > 0, z ε D, for some φ ∈ R. We shall investigate the integral transform V_{λ}(f)(z) = ∫_{0}^{1} λ(t) f(tz)/t dt, where λ is a nonnegative real valued function normalized by ∫_{0}^{1}λ(t)dt = 1. From our main results we get conditions on the number β and the function λ such that V_{λ}(f) is starlike of order μ (0≤μ≤½ ) when f ∈ P_{γ}(β). As applications we study various choices of λ(t), related to classical integral transforms.

Item Type: | Article |
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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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