On the coefficients of some classes of starlike functions
Ryszard Mazur (1983)
Annales Polonici Mathematici
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Ryszard Mazur (1983)
Annales Polonici Mathematici
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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.
Soni, Anil K. (1982)
International Journal of Mathematics and Mathematical Sciences
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M. Obradović, S. Owa (1989)
Matematički Vesnik
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Sanford S. Miller (1976)
Annales Polonici Mathematici
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Milutin Obradović, M. K. Aouf, Shigeyoshi Owa (1989)
Publications de l'Institut Mathématique
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Cz. Bucka, K. Ciozda (1973)
Annales Polonici Mathematici
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S. Owa, M. Obradović (1986)
Matematički Vesnik
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Todorov, Pavel G (2015-12-08T12:45:07Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Romuald Zawadzki (1971)
Annales Polonici Mathematici
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Richard Fournier (1986)
Annales Polonici Mathematici
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Krushkal, Samuel L. (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Bajpai, S.K. (1981)
International Journal of Mathematics and Mathematical Sciences
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Adam Lecko (1998)
Annales Polonici Mathematici
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We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).