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Mathematica Slovaca

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Volume 67, Issue 4

Issues

Hankel determinant for a class of analytic functions involving conical domains defined by subordination

Srinivasan Annamalai
  • Department of Economics and Statistics Office of the Assistant Director of Statistics Tindivanam Division Villupuram, Tamil Nadu 604 001, India
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/ Srikandan Sivasubramanian
  • Department of Mathematics University College of Engineering Tindivanam Anna University Tindivanam, Tamil Nadu 604 001, India
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/ Chellakutty Ramachandran
  • Department of Mathematics University College of Engineering Villupuram Anna University Villupuram, Tamil Nadu 605 602, India
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Published Online: 2017-07-14 | DOI: https://doi.org/10.1515/ms-2017-0023

Abstract

Domains with conical sections is an underlying concept in the area of complex function theory although is an interesting topic and it deserves more attention. There has been many works focusing towards this area for the past two decades. However, the concept of Hankel determinant has not been studied so far. Exploiting this, we provide an estimate for the Hankel determinant with domains bounded by conical sections. The authors sincerely hope this article will revive and encourage the other researchers to obtain similar sort of estimates for other classes connected with conical domains. The concept of conical domains was introduced by Kanas and Wiśniowska.

MSC 2010: Primary 30C45; 33C50; Secondary 30C80

Keywords: analytic function; univalent function; Hankel determinant; differential subordination and conical region

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About the article

*1

The author would like to thank the referee(s) for their critical comments and the Editor for many insightful suggestions that essentially improved the paper. The second-named is supported by a grant from the Department of Science and Technology of the Government of India (vide ref: SR/FTP/MS-022/2012) under its Young Faculty Fast Track Scheme.


Received: 2015-05-08

Accepted: 2015-10-07

Published Online: 2017-07-14

Published in Print: 2017-08-28


Citation Information: Mathematica Slovaca, Volume 67, Issue 4, Pages 945–956, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0023.

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