[Authors]
 V. A. Malyshev

[Title]
 Estimations of derivatives of $n$-convex functions

[AMS Subj-class]
 26-06 Proceedings, conferences, collections
 26A48 Monotonic functions, generalizations
 26A51 Convexity, generalizations
 26D10 Inequalities involving derivatives and differential and
       integral operators
       
[Abstract]
 Estimations of the kind
 $$\begin{array}{lll}
  \|u'-u_0'\|_{C[a+\delta,b-\delta]}&\le&
  A\|u-u_0\|_{C[a,b]}\delta^{-1}+
  B\|u_0^{(n)}\|_{C[a,b]}\delta^ {n-1},\medskip\\
  \|u^{(k)}-u_0^{(k)}\|_{C[a+\delta,b-\delta]}&\le&
  C\|u - u_0\|_{C[a,b]}^{(n-k)/n},\medskip\\
  \|u-u_0\|_{C[a+\delta,b-\delta]}&\le&
  C\|u-u_0\|_{L_1[a,b]}^{n/(n+1)}
 \end{array} $$
 are obtained for $n$-convex functions.

[Keywords]
 Convex functions

[Comments]
 LaTeX, 8 pp., English

[Contact e-mail]
 wmal@ryb.adm.yar.ru