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Probl. Anal. Issues Anal., 2020, Volume 9(27), Issue 2, Pages 119–137 (Mi pa300)  

Zalcman conjecture and Hankel determinant of order three for starlike and convex functions associated with shell-like curves

V. Suman Kumara, R. Bharavi Sharmab

a Department of Mathematics, TSMS, Chigurumamidi, Karimnagar, Telangana-505481, India
b Department of Mathematics, Kakatiya University, Warangal, Telangana-506009, India

Abstract: The aim of this article is to estimate an upper bound of $|H_3(1)|$, the Zalcman coefficient functional for $n=3$ and $n=4$, and also to investigate the fifth, sixth, seventh coefficients of starlike and convex functions associated with shell-like curves. Similar type of outcomes are estimated for the functions $f^{-1} $ and $\frac{z}{f(z)}$.

Keywords: analytic function, function with positive real part, starlike function, subordination, Zalcman conjecture, shell-like curve, Hankel determinant.

Funding Agency Grant Number
Department of Science and Technology, India SR/FST/MSI-101/2014
The work presented in this paper is partially supported by DST/FIST grant no: SR/FST/MSI-101/2014, dated:14-01-2016.


DOI: https://doi.org/10.15393/j3.art.2020.6950

Full text: PDF file (497 kB)
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Bibliographic databases:

UDC: 517.546, 517.547
MSC: Primary 30C45; Secondary 30C50, 30C80
Received: 07.09.2019
Revised: 28.02.2020
Accepted:03.03.2020
Language:

Citation: V. Suman Kumar, R. Bharavi Sharma, “Zalcman conjecture and Hankel determinant of order three for starlike and convex functions associated with shell-like curves”, Probl. Anal. Issues Anal., 9(27):2 (2020), 119–137

Citation in format AMSBIB
\Bibitem{SumBha20}
\by V.~Suman Kumar, R.~Bharavi Sharma
\paper Zalcman conjecture and Hankel determinant of order three for starlike and convex functions associated with shell-like curves
\jour Probl. Anal. Issues Anal.
\yr 2020
\vol 9(27)
\issue 2
\pages 119--137
\mathnet{http://mi.mathnet.ru/pa300}
\crossref{https://doi.org/10.15393/j3.art.2020.6950}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000541846500008}


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