Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination

Ying Yang; Jin-Lin Liu; Ying Yang; Jin-Lin Liu

doi:10.3934/math.2021248

AIMS Mathematics

2021, Volume 6, Issue 4: 4197-4210. doi: 10.3934/math.2021248

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Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination

Ying Yang ¹,
Jin-Lin Liu ^{2
,
,}

1.
Department of Mathematics, Maanshan Teacher's College, Maanshan 243000, China
2.
Department of Mathematics, Yangzhou University, Yangzhou 225002, China

Received: 23 December 2020 Accepted: 03 February 2021 Published: 07 February 2021
MSC : 30C45, 30C80

A new subclass $ \mathcal{G}_n(A, B, \lambda) $ of meromorphically multivalent functions defined by the first-order differential subordination is introduced. Some geometric properties of this new subclass are investigated. The sharp upper bound on $ |z| = r < 1 $ for the functional $ \mathrm{Re}\{(1-\lambda)z^pf(z)-\frac{\lambda}{p}z^{p+1}f'(z)\} $ over the class $ \mathcal{G}_n(A, B, 0) $ is obtained.
- analytic function,
- meromorphically multivalent function,
- differential subordination,
- coefficient estimate,
- sharp bound
Citation: Ying Yang, Jin-Lin Liu. Some geometric properties of certain meromorphically multivalent functions associated with the first-order differential subordination[J]. AIMS Mathematics, 2021, 6(4): 4197-4210. doi: 10.3934/math.2021248

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Abstract

A new subclass $ \mathcal{G}_n(A, B, \lambda) $ of meromorphically multivalent functions defined by the first-order differential subordination is introduced. Some geometric properties of this new subclass are investigated. The sharp upper bound on $ |z| = r < 1 $ for the functional $ \mathrm{Re}\{(1-\lambda)z^pf(z)-\frac{\lambda}{p}z^{p+1}f'(z)\} $ over the class $ \mathcal{G}_n(A, B, 0) $ is obtained.

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