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- Title
On a general bilinear functional equation.
- Authors
Bahyrycz, Anna; Sikorska, Justyna
- Abstract
Let X, Y be linear spaces over a field K . Assume that f : X 2 → Y satisfies the general linear equation with respect to the first and with respect to the second variables, that is, for all x , x i , y , y i ∈ X and with a i , b i ∈ K \ { 0 } , A i , B i ∈ K ( i ∈ { 1 , 2 } ). It is easy to see that such a function satisfies the functional equation for all x i , y i ∈ X ( i ∈ { 1 , 2 } ), where C 1 : = A 1 B 1 , C 2 : = A 1 B 2 , C 3 : = A 2 B 1 , C 4 : = A 2 B 2 . We describe the form of solutions and study relations between (∗) and (∗ ∗) .
- Subjects
FUNCTIONAL equations; VECTOR spaces; LINEAR equations; ADDITIVE functions; BILINEAR forms
- Publication
Aequationes Mathematicae, 2021, Vol 95, Issue 6, p1257
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-021-00819-5