On uniformly starlike functions

Goodman, A. W.

doi:10.1016/0022-247x(91)90006-l

Cited by 204 publications

(124 citation statements)

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“…We note [3] that the classical Alexander's result, / G K <i => zf G S* does not hold between the classes UCV and UST. Later on, Ronning [8] introduced a new class Sp of starlike functions related to UCV defined as (1.5) Note that…”

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confidence: 72%

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On Partial Sums of Certain Analytic Functions

Mostafa¹

2008

Demonstratio Mathematica

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Abstract. In the present paper we give some results concerning partial sums of certain analytic functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. All the results are sharp. IntroductionLet S denote the class of functions of the form:that are analytic (hence the series in (1.1) is convergent), and / is univalent in the open unit disc U = {z = \z\ < 1}. Let K(a) and S*(a) denote the subclasses of S that are, respectively, convex and starlike functions of order a, 0 < a < 1. For conveniece, we write K (

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confidence: 72%

“…Srivastava an Owa [12]). Goodman ([2] and [3]) defined the following subclasses of K and S*. DEFINITION …”

Section: Introductionmentioning

confidence: 99%

On Partial Sums of Certain Analytic Functions

Mostafa¹

2008

Demonstratio Mathematica

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“…[3] Sharp starlikeness conditions 305 Our aim in this paper is to generalize Theorem 1.1 in various ways that enable us to obtain sharp bounds for other types of starlikeness. One obvious generalization of Theorem 1.1, which we do not include, is to get bounds for starlikeness of order a (Re zf'(z)/f (z) > a).…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Sharp starlikeness conditions for analytic functions with bounded derivative

Rønning¹,

Ruscheweyh²,

Samaris³

2000

J Aust Math Soc A

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“…The This improves the bound AI < 1/(ln) of Goodman [1]. It does not appear to be the best possible except when n 2.…”

Section: Introductionmentioning

confidence: 83%

“…This class was recently introduced and s[udied by A.W. Goodman [1] who proved in particular the following analytic characterization. Properties of the class UST are difficult to establish.…”

Section: Introductionmentioning

confidence: 99%