Meromorphic starlike functions

Eenigenburg, P. J.; Livingston, Albert E.

doi:10.1216/rmj-1981-11-3-441

Cited by 5 publications

(9 citation statements)

References 14 publications

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“…The case X = 1 gives us some information on the arc length of the image of the circle \z -p\ = r, 0 < r < 1 -p, for a function/(z) in A*(p). Sharp results concerning the length of the image of \z\ = r, 0 < r < 1, were obtained in [1].…”

Section: Integral Means Of the Derivative And Arc Lengthmentioning

confidence: 99%

“…Integral means of higher order derivatives. We will make use of a method employed by Feng and MacGregor [2] and also utilized in [1], to discuss the integral means JfJ/°°0> + re ie )\ x dd, X ^ 1, 0 < r < (1 -p). We first need two lemmas similar to those proven in [1].…”

Section: Corollary Iff(z) Is In A*{p\ Thenmentioning

confidence: 99%

“…We will make use of a method employed by Feng and MacGregor [2] and also utilized in [1], to discuss the integral means JfJ/°°0> + re ie )\ x dd, X ^ 1, 0 < r < (1 -p). We first need two lemmas similar to those proven in [1]. Again in this section letters signifying constants do not necessarily have the same value each time they appear.…”

Section: Corollary Iff(z) Is In A*{p\ Thenmentioning

confidence: 99%

“…[8]. In [1] it was proven that A*(p) is equivalent to the class of functions /(z) which have the representation (1.1) f(z) = -pzg(z)/(z -p){\ -pz)…”

mentioning

confidence: 99%

“…where we have used the fact that \b-i\ To see that the order is best possible, we note that if have been discussed in [1] and [6].…”

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confidence: 99%

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A class of meromorphic starlike functions

Livingston¹

1983

Rocky Mountain J. Math.

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Let A*(p) be the class of functions/(z) univalent and meromorphic in A = [z/\z\ < 1} with simple pole at z -p, 0 < p < l,/(0) = 1 and which map A onto a domain whose complement is starlike with respect to the origin. We discuss the integral means S-x\f(p + re ie )\ x dO, ~oo<^ 0 are the best possible. Estimates on SU I f w (p + re ie ) | *d0 9 n = 1,2, ..., X > 1 are also obtained. This paper was written during the author's sabbatical leave spent at the University of North Carolina.

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Section: Integral Means Of the Derivative And Arc Lengthmentioning

confidence: 99%

Section: Corollary Iff(z) Is In A*{p\ Thenmentioning

confidence: 99%

Section: Corollary Iff(z) Is In A*{p\ Thenmentioning

confidence: 99%

“…[8]. In [1] it was proven that A*(p) is equivalent to the class of functions /(z) which have the representation (1.1) f(z) = -pzg(z)/(z -p){\ -pz)…”

mentioning

confidence: 99%

“…where we have used the fact that \b-i\ To see that the order is best possible, we note that if have been discussed in [1] and [6].…”

mentioning

confidence: 99%

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