摘要:

The paper contains a biographical profile of A. W. Goodman, a review of his main results and the complete list of his published research papers and books.

ISSN:0278-1077    

DOI:10.1080/17476939708815008

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In his paper [2] Lowell J. Hansen found a (nonlinear) recurrence formula for the (sharp constant appearing in the “Ring Lemma” of Rodin and Sullivan [3].

ISSN:0278-1077    

DOI:10.1080/17476939708815009

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this article we introduce the tamily ε(α), α ∈C. ofα-exponentially convexfunctionsfas normalized univalent functions in the unit diskDsuch thateαfis convex univalent. Out study was suggested by a formal and concrete relationship between ε(α) and the classof convex functions of bounded type, defined by Professor A. W. Goodman. We also exhibit the connections to the classC(α) of normalized convex univalent functions which omit the balue -1/α.C-C(0) and to the classCH(α) of normalized convex univalent functions whose ranges lie mside a horizontal strip of width φ/α. Beside the description of some basic geometrical and analytic properties of the functions in ε(α). we are mainly interested in the determination of various Koebe domains or Koebe radii. We solve (up to certain constrained minimizations the Koebe radius and Koebe domain problem forC∩ε(α) andCH(α), and the Koebe domain problems forC(α) and ε(α) Because of technical difficulties this cannot be used to obtain the sharp (explicit) Koebe radius for ε(α). We have, however, complete numerical results. At least we can show that the Koebe radius forC∩ε(α) is larger than the one for ε(α), for small α

ISSN:0278-1077    

DOI:10.1080/17476939708815010

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In 1972. D.A. Branna conjectured that all of the odd coefficients,a2n+1of the power series (1+xz)α/(1-z) were dominated by those of the series (1 +z)α(1-z) for the parameter range 0 < α < 1 after having shown that this was not true for the even coefficients. He verified the case when 2n+ 1 = 3 The case when 2n+ 1 = 5 was verified in the mid-eighties by J. G. Milcetich. In this paper, we verify the case when 2n+ l = 7 using classical Sturm sequence arguments and some computer algebra.

ISSN:0278-1077    

DOI:10.1080/17476939708815011

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We investigate whether the conditionssufficient for a functionthat is analytic and locally univalent to be univalent in the unit diskUcan be weakened by allowing the above three expressions to lie in a larger domain of variability. It turns out that in various cases the functionfcan then be infinitely valent inU.

ISSN:0278-1077    

DOI:10.1080/17476939708815012

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939708815013

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The classSnconsists of univalent, harmonic, and sense-preserving functionsJunit disk δ such thatwhere. Using a technique from Clinic and Shell-Small, we construct a family of I-slit mappings inSpby varying. AsW(z)changes, the tin of the slit slides along the negative real axis from the point U to - 1 In doing so. we establish that the inner mapping radiusp(f)can be as large as 4. In addition, we show that the inner mapping radius for functions incan be as small as 1/2 and as large as 2.

ISSN:0278-1077    

DOI:10.1080/17476939708815014

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

If a sense-preserving harmonic mapping has dilatation of unit modulus on some boundary are, then it maps that are onto a concave are unless it is piecewise constant A theorem to this effect is proved with the aid of Hopf's lemma. A corollary is that if a harmonic mapping of the disk onto a convex domain extends to a “regular” homeomorphism of the closures, then it is quasiconformal.

ISSN:0278-1077    

DOI:10.1080/17476939708815015

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We investigate some coefficient properties of univalent functions related to their Grunsky operators and quasiconformal extendibility. We find some bounds of the sharp growth order innand numerical estimates for coefficient differences of analytic and univalent functions in the unit disk. These results depend on a restriction of the norm of the Grunsky operator.

ISSN:0278-1077    

DOI:10.1080/17476939708815016

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

This paper studies the tangential limit of functions defined byWhere μ is a complex valued Borel measure the results depend on local properties of the measure μ Various tangential limits associated withfare shown to hold off exceptional sets.

ISSN:0278-1077    

DOI:10.1080/17476939708815017

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor