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- Title
On a class of linear functional equations without range condition.
- Authors
Gselmann, Eszter; Kiss, Gergely; Vincze, Csaba
- Abstract
The main purpose of this work is to provide the general solutions of a class of linear functional equations. Let n ≥ 2 be an arbitrarily fixed integer, let further X and Y be linear spaces over the field K and let α i , β i ∈ K , i = 1 , ... , n be arbitrarily fixed constants. We will describe all those functions f , f i , j : X × Y → K , i , j = 1 , ... , n that fulfill the functional equation f ∑ i = 1 n α i x i , ∑ i = 1 n β i y i = ∑ i , j = 1 n f i , j (x i , y j) x i ∈ X , y i ∈ Y , i = 1 , ... , n. Additionally, necessary and sufficient conditions will also be given that guarantee the solutions to be non-trivial.
- Subjects
FUNCTIONAL equations; LINEAR equations; VECTOR spaces; ADDITIVE functions
- Publication
Aequationes Mathematicae, 2020, Vol 94, Issue 3, p473
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-019-00672-7