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Research Article | Open Access

Bi-univalent functions of complex order defined by Hohlov operator associated with legendrae polynomial

Gangadharan Murugusundaramoorthy1, Luminiţa-Ioana Cotîrlă2( )
School of Advanced Sciences, VIT University, Vellore 632014, Tamilnadu, India
Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania
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Abstract

In this paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

Keywords

analytic functionsunivalent functionsbi-univalent functionsbi-starlike and bi-convex functionsHohlov operatorgaussian hypergeometric functionDziok-Srivastava operatorlegendrae polynomial
CLC number: 30C45, 30C50, 30C55, 30C80

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8733-8750
DOI: 10.3934/math.2022488

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Cite this article:
Murugusundaramoorthy G, Cotîrlă L-I. Bi-univalent functions of complex order defined by Hohlov operator associated with legendrae polynomial. AIMS Mathematics, 2022, 7(5): 8733-8750. https://doi.org/10.3934/math.2022488

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Received: 22 December 2021
Revised: 25 January 2022
Accepted: 10 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)