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Density covers

A. M. Bruckner, Charles L. Thorne (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Differentiability of Polynomials over Reals

Artur Korniłowicz (2017)

Formalized Mathematics

In this article, we formalize in the Mizar system [3] the notion of the derivative of polynomials over the field of real numbers [4]. To define it, we use the derivative of functions between reals and reals [9].

Differentiation of n-convex functions

H. Fejzić, R. E. Svetic, C. E. Weil (2010)

Fundamenta Mathematicae

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.

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