Glasnik Matematicki, Vol. 32, No.1 (1997), 29-37.

SOME REFINEMENTS OF BERNSTEIN-TYPE INEQUALITIES FOR RATIONAL FUNCTIONS

Abdul Aziz and W. M. Shah

Post-graduate Department of Mathematics, University of Kashmir, Hazratbal, Srinagar - 190 006, Kashmir, India


Abstract.   In this paper we establish some refinements of Bernstein-type inequalities for rational functions with prescribed poles and restricted zeros, which generalizes the corresponding refinements of some polynomial inequalities due to Erdos-Lax, Turan and others. Generalization of a result of O'Hara and Rodriguez concerning self-inversive polynomials is also obtained for self-inversive rational functions.

1991 Mathematics Subject Classification.   26D07.

Key words and phrases.   Inequalities in a complex domain, self-inversive rational function, polynomials, extremal problems.


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