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For $k \in ℕ \cup {\infty}$ and $U$ open in $ℝ$ , let $C^{k} (U)$ be the ring of real valued functions on $U$ with the first $k$ derivatives continuous. It is shown that for $f \in C^{k} (U)$ there is $g \in C^{\infty} (ℝ)$ with $U \subseteq coz g$ and $h \in C^{k} (ℝ)$ with ${f g |}_{U} {= h |}_{U}$ . The function $f$ and its $k$ derivatives are not assumed to be bounded on $U$ . The function $g$ is constructed using splines based on the Mollifier function. Some consequences about the ring $C^{k} (ℝ)$ are deduced from this, in particular that $Q_{cl} (C^{k} (ℝ)) = Q (C^{k} (ℝ))$ .

On extreme first return path derivatives

Aliasghar Alikhani-Koopaei (2002)

Mathematica Slovaca

On functions of bounded n-th variation

S. Mukhopadhyay, D. Sain (1988)

Fundamenta Mathematicae

On generalized Peano and Peano derivatives

H. Fejzić (1993)

Fundamenta Mathematicae

A function F is said to have a generalized Peano derivative at x if F is continuous in a neighborhood of x and if there exists a positive integer q such that a qth primitive of F in the neighborhood has the (q+n)th Peano derivative at x; in this case the latter is called the generalized nth Peano derivative of F at x and denoted by $F_{[n]} (x)$ . We show that generalized Peano derivatives belong to the class [Δ’]. Also we show that they are path derivatives with a nonporous system of paths satisfying the I.I.C....

On Köpcke and Pompeiu functions

Jaroslav Blažek, Emil Borák, Jan Malý (1978)

Časopis pro pěstování matematiky

On Kurzweil-Stieltjes equiintegrability and generalized BV functions

Giselle A. Monteiro (2019)

Mathematica Bohemica

We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.

On level sets of approximate derivative and approximate symmetric derivative

H. H. Pu, H. W. Pu (1987)

Colloquium Mathematicae

On majorization, favard and Berwald inequalities.

Latif, Naveed, Pečarić, J., Perić, I. (2011)

Annals of Functional Analysis (AFA) [electronic only]

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