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Central functions for classes of concave univalent functions

  • Bappaditya Bhowmik EMAIL logo and Karl-Joachim Wirths
Published/Copyright: April 26, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In this paper we answer a question of Bednarz and Sokól concerning concave univalent functions. We prove that there exist central functions for the classes Co(p) of concave univalent functions with pole at the point z = p ∈ (0, 1). Further, we construct a generalized neighborhood of this central function such that the whole class Co(p) is contained in such neighborhood. We also consider similar questions for the class of functions that are analytic and univalent in the unit disc and for some of its important subclasses.

Keywords: central function; concave univalent function; neighborhoods of analytic functions; Primary 30C45
MSC: Primary 30C45

The first author of this article would like to thank NBHM, DAE, India (Ref. No. - NBHM/R.P.54/2012/Fresh/304) for its financial support.

  1. This paper has been communicated by Ján Borsík

References

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Received: 2013-1-16
Accepted: 2013-5-15
Published Online: 2016-4-26
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0124
Keywords for this article
central function; concave univalent function; neighborhoods of analytic functions; Primary 30C45

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
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  5. Research Article
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  7. Research Article
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  9. Research Article
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  13. Research Article
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