On second-order differential subordination for certain meromorphically multivalent functions

Cai-Mei Yan; Jin-Lin Liu; Cai-Mei Yan; Jin-Lin Liu

doi:10.3934/math.2020320

AIMS Mathematics

2020, Volume 5, Issue 5: 4995-5003. doi: 10.3934/math.2020320

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Research article

On second-order differential subordination for certain meromorphically multivalent functions

Cai-Mei Yan ¹,
Jin-Lin Liu ^{2
,
,}

1.
Information Engineering College, Yangzhou University, Yangzhou 225002, China
2.
Department of Mathematics, Yangzhou University, Yangzhou 225002, China

Received: 18 April 2020 Accepted: 22 May 2020 Published: 09 June 2020
MSC : Primary 30C45; Secondary 30C80

A new class $\mathcal{R}_n(A, B, \lambda)$ of meromorphically multivalent functions defined by the second-order differential subordination is introduced. Several geometric properties of this new class are studied. The sharp upper bound on $|z| = r < 1$ for the functional $\mathrm{Re}\{(\lambda-1)z^{p+1}f'(z)+\frac{\lambda}{p+1}z^{p+2}f''(z)\}$ over the class $\mathcal{R}_n(A, B, 0)$ is obtained.
- meromorphically multivalent function,
- differential subordination,
- coefficient estimate,
- sharp bound
Citation: Cai-Mei Yan, Jin-Lin Liu. On second-order differential subordination for certain meromorphically multivalent functions[J]. AIMS Mathematics, 2020, 5(5): 4995-5003. doi: 10.3934/math.2020320

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Abstract

A new class $\mathcal{R}_n(A, B, \lambda)$ of meromorphically multivalent functions defined by the second-order differential subordination is introduced. Several geometric properties of this new class are studied. The sharp upper bound on $|z| = r < 1$ for the functional $\mathrm{Re}\{(\lambda-1)z^{p+1}f'(z)+\frac{\lambda}{p+1}z^{p+2}f''(z)\}$ over the class $\mathcal{R}_n(A, B, 0)$ is obtained.

References

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