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2014 | OriginalPaper | Buchkapitel

7. Starlikeness and Convexity of Certain Integral Transforms by using Duality Technique

verfasst von : Satwanti Devi, A. Swaminathan

Erschienen in: Current Topics in Pure and Computational Complex Analysis

Verlag: Springer India

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Abstract

Duality technique is applied on the integral transform of the type \(V_\lambda(f)(z)=\int_0^1\lambda(t)\frac{f(tz)}{t}{} dt\), where \(\int_0^1 \lambda(t)dt =1\) and f is functional class that satisfies certain analytic characterization in the unit disk. This leads to the investigation between the equivalence of non-negativity of a linear functional and the given integral transform involving starlike and convex functions. Particular values of \(\lambda(t)\) give rise to well-known integral operators. Investigation of the parameters for such values leads to interesting results in univalent function theory. This chapter outlines all the possible results available in the literature in this direction to provide the reader an overview.

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Titel: Starlikeness and Convexity of Certain Integral Transforms by using Duality Technique
verfasst von: Satwanti Devi
A. Swaminathan
Verlag: Springer India
Buch: Current Topics in Pure and Computational Complex Analysis
Print ISBN: 978-81-322-2112-8

Electronic ISBN: 978-81-322-2113-5

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-81-322-2113-5_7

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