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On a functional equation characterizing linear similarities.
- Source :
-
Aequationes Mathematicae . Jun2019, Vol. 93 Issue 3, p557-561. 5p. - Publication Year :
- 2019
-
Abstract
- The aim of this paper is to give an answer to a question posed by Alsina, Sikorska and Tomás. Namely, we show that, under suitable assumptions, a function f : X → Y from a normed space X into a normed space Y, satisfying the functional equation f y - ρ + ′ (x , y) ‖ x ‖ 2 x = f (y) - ρ + ′ (f (x) , f (y)) ‖ f (x) ‖ 2 f (x) , x , y ∈ X has to be a linear similarity (scalar multiple of a linear isometry). [ABSTRACT FROM AUTHOR]
- Subjects :
- *FUNCTIONAL equations
*LINEAR equations
*NORMED rings
*RESEMBLANCE (Philosophy)
Subjects
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 93
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 136731644
- Full Text :
- https://doi.org/10.1007/s00010-018-0603-2