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

Gangadharan Murugusundaramoorthy; Luminiţa-Ioana Cotîrlă; Gangadharan Murugusundaramoorthy; Luminiţa-Ioana Cotîrlă

doi:10.3934/math.2022488

AIMS Mathematics

2022, Volume 7, Issue 5: 8733-8750. doi: 10.3934/math.2022488

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Research article

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

Gangadharan Murugusundaramoorthy ¹,
Luminiţa-Ioana Cotîrlă ^{2
,
,}

1.
School of Advanced Sciences, VIT University, Vellore 632014, Tamilnadu, India
2.
Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania

Received: 22 December 2021 Revised: 25 January 2022 Accepted: 10 February 2022 Published: 03 March 2022
MSC : 30C45, 30C50, 30C55, 30C80

In this paper, we introduce and investigate two new subclasses of the function class $ \Sigma $ 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.
- analytic functions,
- univalent functions,
- bi-univalent functions,
- bi-starlike and bi-convex functions,
- Hohlov operator,
- gaussian hypergeometric function,
- Dziok-Srivastava operator,
- legendrae polynomial
Citation: Gangadharan Murugusundaramoorthy, Luminiţa-Ioana Cotîrlă. Bi-univalent functions of complex order defined by Hohlov operator associated with legendrae polynomial[J]. AIMS Mathematics, 2022, 7(5): 8733-8750. doi: 10.3934/math.2022488

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Abstract

In this paper, we introduce and investigate two new subclasses of the function class $ \Sigma $ 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.

References

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