On the Cauchy equation on spheres

Roman Ger; Justyna Sikorska

Published: 1997-09-30

Vol. 11 (1997)

On the Cauchy equation on spheres

Roman Ger , Justyna Sikorska

Abstract

We deal with a conditional functional equation
ϕ(x) = ϕ(y) implies f(x+y) = f(x)+f(y).
Under some assumptions imposed on function ϕ, the domains and ranges of ϕ and f we derive the additivity of f. As a consequence we obtain two Hyers-Ulam stability results related to the equation considered.

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Ger, R., & Sikorska, J. (1997). On the Cauchy equation on spheres. Annales Mathematicae Silesianae, 11, 89–99. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14186

Roman Ger

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

Justyna Sikorska

Affiliation:

Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland

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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