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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.