The Fekete-Szegö type inequalities for certain subclasses analytic functions associated with petal shaped region

Pinhong Long; Xing Li; Gangadharan Murugusundaramoorthy; Wenshuai Wang; Pinhong Long; Xing Li; Gangadharan Murugusundaramoorthy; Wenshuai Wang

doi:10.3934/math.2021357

AIMS Mathematics

2021, Volume 6, Issue 6: 6087-6106. doi: 10.3934/math.2021357

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Research article

The Fekete-Szegö type inequalities for certain subclasses analytic functions associated with petal shaped region

Pinhong Long ^{1
,
,},
Xing Li ¹,
Gangadharan Murugusundaramoorthy ^{2
,
,},
Wenshuai Wang ¹

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia 750021, China
2.
Department of Mathematics, VIT University, Vellore, Tamil Nadu 632014, India

Received: 05 December 2020 Accepted: 17 March 2021 Published: 01 April 2021
MSC : 30C45, 30C50

In the article we introduce several new subclasses of analytic functions associated with pedal shaped functions. By using differential subordination and convolution operator theory, we obtain the bound estimations of the coefficients $ a_2 $ and $ a_3 $, and the logarithmic coefficients $ d_1 $ and $ d_2 $ as well as Fekete-Szegö type functional inequalities for these subclasses.
- Fekete-Szegö problem,
- univalent function,
- subordination,
- pedal shaped function
Citation: Pinhong Long, Xing Li, Gangadharan Murugusundaramoorthy, Wenshuai Wang. The Fekete-Szegö type inequalities for certain subclasses analytic functions associated with petal shaped region[J]. AIMS Mathematics, 2021, 6(6): 6087-6106. doi: 10.3934/math.2021357

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Abstract

In the article we introduce several new subclasses of analytic functions associated with pedal shaped functions. By using differential subordination and convolution operator theory, we obtain the bound estimations of the coefficients $ a_2 $ and $ a_3 $, and the logarithmic coefficients $ d_1 $ and $ d_2 $ as well as Fekete-Szegö type functional inequalities for these subclasses.

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