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Univalence and starlikeness of nonlinear integral transform of certain class of analytic functions
Published in Indian Academy of Sciences
2009
Volume: 119
   
Issue: 5
Pages: 593 - 610
Abstract
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition For f ∈ U(λ, μ) with μ ≤ 1 and 0 ≠ μ1 ≤ 1, and for a positive real-valued integrable function φ defined on [0,1] satisfying the normalized condition _ 1 0 φ(t) dt = 1, we consider the transform Gφf (z) defined by In this paper, we find conditions on the range of parameters λ and μ so that the transform Gφf is univalent or star-like. In addition, for a given univalent function of certain form, we provide a method of obtaining functions in the class U(λ, μ). © Printed in India.
About the journal
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
PublisherIndian Academy of Sciences
ISSN02534142
Open AccessNo
Concepts (12)
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    Functional analysis
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    Integral equations
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    Stars
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    ANALYTIC FUNCTIONS
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    INTEGRABLE FUNCTIONS
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    Integral transform
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    NONLINEAR INTEGRAL TRANSFORMS
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    STAR-LIKE
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    UNIT DISK
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    UNIVALENT
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    UNIVALENT FUNCTION
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    Functions