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Probl. Anal. Issues Anal., 2021, Volume 10(28), Issue 1, Pages 69–86 (Mi pa317)  

Harmonic mappings with the fixed analytic part

Rajbala, Jugal K. Prajapat

Department of Mathematics, Central University of Rajasthan, Bandarsindri, Kishangarh-305817, Dist.-Ajmer, Rajasthan, India

Abstract: In this article, we consider a class of sense-preserving harmonic mappings whose analytic part is convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Further, we obtain bounds on pre-Schwarzian derivatives and bounds on the Bloch's constant. Finally, we obtain coefficient bounds, growth and distortion results.

Keywords: univalent harmonic mappings, functions convex in one direction, pre-Schwarzian derivative, Bloch's constant, coefficient bound, growth and distortion results.

DOI: https://doi.org/10.15393/j3.art.2021.8850

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Bibliographic databases:

UDC: 517.54
MSC: 30C45, 30C80
Received: 29.07.2020
Revised: 16.12.2020
Accepted:17.12.2020
Language:

Citation: Rajbala, Jugal K. Prajapat, “Harmonic mappings with the fixed analytic part”, Probl. Anal. Issues Anal., 10(28):1 (2021), 69–86

Citation in format AMSBIB
\Bibitem{RajPra21}
\by Rajbala, Jugal~K.~Prajapat
\paper Harmonic mappings with the fixed analytic part
\jour Probl. Anal. Issues Anal.
\yr 2021
\vol 10(28)
\issue 1
\pages 69--86
\mathnet{http://mi.mathnet.ru/pa317}
\crossref{https://doi.org/10.15393/j3.art.2021.8850}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000621661400005}


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