English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The following Bernstein inequality max |z| 1 |p′(z)| n max |z| 1 |p(z)|, valid for all complex polynomials p of degree n , has been extended by Ruscheweyh to max |z| 1 |p′(z)| n max |z| 1 |p(z)| − 2n n + 2 |p(0)|, n 2. We prove in this note that two other Bernstein inequalities, i.e., max −1 x 1 ∣ ∣ ∣ √ 1 − x2p′(x) ∣ ∣ ∣ n max −1 x 1 |p(x)| or max 0 θ 2π |t′(θ)| n max 0 θ 2π |t(θ)|, where t(θ) is a complex trigonometric polynomial of degree n do not admit similar extensions. In addition we obtain a new proof of Marcel Riesz interpolation formula. Mathematics subject classification (2000): 41A17.

On an improvement of Bernstein's polynomial inequalities