Displaying similar documents to “On certain classes of analytic functions”

Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator

M. Aouf, A. Shamandy, A. Mostafa, S. Madian (2010)

Annales UMCS, Mathematica

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Let A denote the class of analytic functions with the normalization f(0) = f'(0) - 1 = 0 in the open unit disc U = {z : |z| < 1}. Set [...] and define ∞nλ, μ in terms of the Hadamard product [...] . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by [...] . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Inclusion properties of certain subclass of analytic functions defined by multiplier transformations

Mohamed Aouf, Rabha El-Ashwah (2009)

Annales UMCS, Mathematica

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Let A denote the class of analytic functions with normalization [...] in the open unit disk [...] Set [...] and define [...] in terms of the Hadamard product [...] In this paper, we introduce several new subclasses of analytic functions defined by means of the operator [...] [...] .Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Inclusion relationships between classes of functions defined by subordination

Jacek Dziok (2011)

Annales Polonici Mathematici

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The purpose of the present paper is to investigate various inclusion relationships between several classes of analytic functions defined by subordination. Many interesting applications involving the well-known classes of functions defined by linear operators are also considered.

Criteria for univalence, starlikeness and convexity

S. Ponnusamy, P. Vasundhra (2005)

Annales Polonici Mathematici

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Let 𝓐 denote the class of all normalized analytic functions f (f(0) = 0 = f'(0)-1) in the open unit disc Δ. For 0 < λ ≤ 1, define 𝓤(λ) = {f ∈ 𝓐 : |(z/f(z))²f'(z) - 1| < λ, z ∈ Δ} and 𝓟(2λ) = f ∈ 𝓐 : |(z/f(z))''| < 2λ, z ∈ Δ.cr Recently, the problem of finding the starlikeness of these classes has been considered by Obradović and Ponnusamy, and later by Obradović et al. In this paper, the authors consider the problem of finding...

On classes of uniformly starlike functions

Agnieszka Wiśniowska-Wajnryb (2013)

Annales Polonici Mathematici

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We geometrically define subclasses of starlike functions related to the class of uniformly starlike functions introduced by A. W. Goodman in 1991. We give an analytic characterization of these classes, some radius properties, and examples of functions in these classes. Our classes generalize the class of uniformly starlike functions, and many results of Goodman are special cases of our results.