Abstract
We identify extremal polynomials for a class of known refinements of Bernstein’s polynomial inequality. For example, the inequality \(\mid zp^\prime (z) - p(z) + p(0)\mid +\mid p(0)\mid \le (n-1) \max_{\mid u\mid \le 1} \mid p(u)\mid,\qquad \mid z\mid \le 1,\) holds for any polynomial p of degree n ≥ 2, and equality holds for some z, ¦z¦ = 1, if and only if p is a monomial of degree n or else p ≢ 0.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
