Balasubramanian, R. ; Ponnusamy, S. ; Prabhakaran, D. J.
(2007)
*Convexity of integral transforms and function spaces*
Integral Transforms and Special Functions, 18
(1).
pp. 1-14.
ISSN 1065-2469

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Related URL: http://dx.doi.org/10.1080/10652460600871426

## Abstract

For β<1, let P_{γ}(β) denote the class of all normalized analytic functions f in the unit disc Δ such that Re{e^{iφ}((1−γ)f(z)/z+γf'(z)-β)}>0, z ∈ Δ, for some φ∈R. Let S^{∗}(μ), 0≤μ<1, denote the usual class of starlike functions of order μ. Define K(μ)={f: zf'(z)∈S^{∗}(μ)}, the class of all convex functions of order μ. In this paper, we consider integral transforms of the form V_{λ} (f)(z) = ∫_{0}^{1}λ(t) f(tz)/t dt and ν_{λ}(f)(z) = z ∫_{0}^{1}λ(t) 1-ρtz/1-tz dt ∗ f(z) . The aim of this paper is to find conditions on λ(t) so that each of the transformations carries P_{γ}(β) into S^{∗}(μ) or K(μ). A number of applications for certain special choices of λ(t) are also established. These results extend the previously known results by a number of authors.

Item Type: | Article |
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Source: | Copyright of this article belongs to Taylor and Francis Ltd. |

Keywords: | Duality; Hypergeometric Functions; Univalent; Starlike and Convex Functions |

ID Code: | 1308 |

Deposited On: | 04 Oct 2010 07:52 |

Last Modified: | 01 Feb 2023 07:20 |

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