Generalization of Some Inequalities for Rational Functions with Prescribed Poles

The main objective of this paper is to establish the modulus of derivative of rational functions r(z) having all its zeros in |z|≤ k ≤1 except t zeros of order α_1, α_2, …..., α_t respectively and some other related inequalities. Besides generalizing and sharpening some well-known inequalities for the derivative of rational functions with prescribed poles, the obtained results also refine some polynomial inequalities.