Differentiation of n-convex functions

• Autorzy: H. Fejzić , R. E. Svetic , C. E. Weil
• Języki publikacji: EN

Abstrakty

EN

The main result of this paper is that if f is n-convex on a measurable subset E of ℝ, then f is n-2 times differentiable, n-2 times Peano differentiable and the corresponding derivatives are equal, and $f^{(n-1)} = f_{(n-1)}$ except on a countable set. Moreover $f_{(n-1)}$ is approximately differentiable with approximate derivative equal to the nth approximate Peano derivative of f almost everywhere.

Kategorie tematyczne

• 26C99: None of the above, but in this section
• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
• 26A51: Convexity, generalizations
• 26A12: Rate of growth of functions, orders of infinity, slowly varying functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 1
• Strony: 9-25

Daty

wydano

2010

Twórcy

autor

H. Fejzić

• Department of Mathematics, California State University, San Bernardino, CA 92407, U.S.A.

autor

R. E. Svetic

• 2022 N. Nevada St., Chandler, AZ 85225, U.S.A.

autor

C. E. Weil

• Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, U.S.A.

Identyfikatory

DOI

10.4064/fm209-1-2