Uniformly Convex Functions and a Corresponding Class of Starlike Functions

Proceedings of the American Mathematical Society (Impact Factor: 0.68). 05/1993; 118(1). DOI: 10.2307/2160026
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Available from: Frode Rønning, Dec 29, 2014
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    • "where g ∈ U CV, which is also in S p , denotes the class of parabolic star like functions introduced by Ronning [9]. Geometrically S p is the class of functions f given (1.1), for which zf (z) f (z) takes its value in the interior of the parabola in the right half plane symmetric about the real axis with vertex at "

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    • ", while zf (z)/f (z) √ 1 + cz was considered in [1]. In [12], Rønning defined the class "

    Comptes Rendus Mathematique 10/2015; DOI:10.1016/j.crma.2015.09.011 · 0.47 Impact Factor
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    • "Moreover, this class for k = 1, corresponds to the class of uniformly convex functions UCV introduced by Goodman [5], which was studied extensively by Rønning [13], and independently also by Ma and Minda [12]. The class k-ST is related to the class k-U CV by means of the well-known Alexander equivalence between the usual classes of convex CV and starlike ST functions (see also the works [1] [8] [10] [7] [12] [13] concerning further developments involving each one of the classes k-U CV and k-ST ). The class k-ST has the geometric characterization (see [11]) that if f ∈ k-ST , then it maps a lens-like domain U (ζ, r) ∩ U (0, R) onto a starlike domain, where U (ζ, r) is a disk of radius r with center ζ , and 0 < R ≤ 1, |ζ | ≤ k, r ≥ |ζ | 2 + R 2 . "
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    ABSTRACT: Our objective in this paper is to consider some basic properties of the familiar Chebyshev polynomials in the theory of analytic functions. We investigate some basic useful characteristics for a class , , of functions f, with , , analytic in the open unit disc satisfying the condition that
    Comptes Rendus Mathematique 03/2015; 353(5). DOI:10.1016/j.crma.2015.02.001 · 0.47 Impact Factor
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