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

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.

Keywords

• meromorphic function
• subordination and majorization