Abstract

Refinement of some Bernstein type inequalities for rational functions

Highlights

  • Let Pn denote the space of complex polynomials n f (z) := ∑︀ ajzj of degree at-most n 1

  • Turan [7] considered the polynomial having all zeros in T ∪ D− and proved the following reverse inequality: If p ∈ Pn has all zeros in T ∪ D−

  • We find some inequalities for rational functions, which, in particular, refine Theorem B and Theorem D for a particular class of rational functions

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Summary

Introduction

Let Pn denote the space of complex polynomials n f (z) := ∑︀ ajzj of degree at-most n 1. For r ∈ Rn, let ‖r‖ = max |r(z)| be the Chebyshev norm of r on T z∈T The inequality (1) is sharp and equality holds for polynomials having all zeros at the origin. Turan [7] considered the polynomial having all zeros in T ∪ D− and proved the following reverse inequality: If p ∈ Pn has all zeros in T ∪ D−,

Results
Conclusion

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