GENERALIZATIONS OF CERTAIN WELL-KNOWN INEQUALITIES FOR RATIONAL FUNCTIONS

Abstract

In this paper we generalize and refine a result of Wali and Shah concerning the estimate of the derivative of the maximum modulus of rational functions with prescribed poles and restricted zeros. The obtained results generalize and sharpen some well-known inequalities for the derivative of rational functions besides the refinement of some polynomial inequalities.

Keywords

• polynomial
• rational function
• 𝑠-fold zeros
• bernsteintype inequality