Majorization problem for two subclasses of meromorphic functions associated with a convolution operator

Akhter Rasheed; Saqib Hussain; Syed Ghoos Ali Shah; Maslina Darus; Saeed Lodhi; Akhter Rasheed; Saqib Hussain; Syed Ghoos Ali Shah; Maslina Darus; Saeed Lodhi

doi:10.3934/math.2020331

AIMS Mathematics

2020, Volume 5, Issue 5: 5157-5170. doi: 10.3934/math.2020331

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Research article

Majorization problem for two subclasses of meromorphic functions associated with a convolution operator

1.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
2.
Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
3.
Department of Management Sciences, COMSATS University Islamabad, Abbottabad Campus, Pakistan

Received: 03 December 2019 Accepted: 25 May 2020 Published: 15 June 2020
MSC : 30C45, 30C50

In the present paper, we investigate a majorization problem for the class $% M_{\alpha, \beta }^{\nu, j}(\eta, \varkappa; A, B)$ of meromorphic functions and the class $N_{\alpha, \beta }^{\nu, j}(\theta, b;A, B)$ of meromorphic spirllike functions related with a convolution operator. We extend the results existing in literature for higher order derivative. Several consequences of the main results in the form of corollaries are also pointed out.
- meromorphic function,
- subordination and majorization
Citation: Akhter Rasheed, Saqib Hussain, Syed Ghoos Ali Shah, Maslina Darus, Saeed Lodhi. Majorization problem for two subclasses of meromorphic functions associated with a convolution operator[J]. AIMS Mathematics, 2020, 5(5): 5157-5170. doi: 10.3934/math.2020331

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Abstract

In the present paper, we investigate a majorization problem for the class $% M_{\alpha, \beta }^{\nu, j}(\eta, \varkappa; A, B)$ of meromorphic functions and the class $N_{\alpha, \beta }^{\nu, j}(\theta, b;A, B)$ of meromorphic spirllike functions related with a convolution operator. We extend the results existing in literature for higher order derivative. Several consequences of the main results in the form of corollaries are also pointed out.

References

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