Perturbations de fonctions additives

Alice Simon; Peter Volkmann

Published: 1997-09-30

Vol. 11 (1997)

Perturbations de fonctions additives

Alice Simon , Peter Volkmann

Abstract

Let α ≥ 0, α ≠ 1 and f: [0,∞[→ℝ be such that f(x+y) = f(x)+f(y)+o(max{x^α,y^α}) as max{x,y}↓0. We show that f(x) = a(x)+o(x^α), where a is an additive function, and we use this result in studying a second order generalized derivative for real functions.

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Simon, A., & Volkmann, P. (1997). Perturbations de fonctions additives. Annales Mathematicae Silesianae, 11, 21–27. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14180

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Alice Simon

Affiliation:

Départment de Mathématiques, Université d'Orléans, France France

Peter Volkmann

Affiliation:

Mathematisches Institut I, Universität Karlsruhe, Allemagne Germany

Vol. 11 (1997)
Published: 1997-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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