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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 34, Issue 2


Radius problems associated with pre-Schwarzian and Schwarzian derivatives

Saminathan Ponnusamy
  • Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India
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/ Swadesh Kumar Sahoo
  • Corresponding author
  • Department of Mathematics, Indian Institute of Technology Indore, M-Block, I.E.T. DAVV Campus, Khandwa Road, Indore 452 017, India
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/ Toshiyuki Sugawa
Published Online: 2014-05-28 | DOI: https://doi.org/10.1515/anly-2012-1219


Some of important univalence criteria for a non-constant meromorphic function f(z) on the unit disk 𝔻 involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss the problem of finding the largest possible r ∈ (0, 1) for which the pre-Schwarzian norm of the dilation r−1f(rz) is not greater than a prescribed number for normalized univalent functions f(z) in the unit disk. Similar results concerning the Schwarzian derivative are also obtained.

Keywords: Univalent functions; radius property; pre-Schwarzian and Schwarzian derivatives; pre-Schwarzian and Schwarzian norms

AMS (2010): Primary 30C45; Secondary 30C55; 33C05

About the article

Accepted: 2014-03-06

Received: 2013-07-10

Published Online: 2014-05-28

Published in Print: 2014-06-28

Citation Information: Analysis, Volume 34, Issue 2, Pages 163–171, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2012-1219.

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