DC pole | Wartość | Język |
dc.contributor.author | Bahyrycz, Anna | - |
dc.contributor.author | Sikorska, Justyna | - |
dc.date.accessioned | 2021-07-15T06:38:01Z | - |
dc.date.available | 2021-07-15T06:38:01Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Aequationes Mathematicae, 2021 | pl_PL |
dc.identifier.issn | 0001-9054 | - |
dc.identifier.issn | 1420-8903 | - |
dc.identifier.uri | http://hdl.handle.net/20.500.12128/20645 | - |
dc.description.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,
{f(a(1)x(1) + a(2)x(2), y) = A(1)f(x(1), y) + A(2)f(x(2), y)
f(x, b(1)y(1) + b(2)y(2)) = B(1)f(x, y(1)) + B(2)f(x, y(2)), (*)
for all x, x(i), y, y(i) is an element of X and with a(i), b(i) is an element of K\{0}, A(i), B-i is an element of K (i is an element of {1, 2}). It is easy to see that such a function satisfies the functional equation
f(a(1)x(1) + a(2)x(2), b(1)y(1) + b(2)y(2)) = C(1)f(x(1), y(1)) + C(2)f(x(1), y(2)) + C(3)f(x(2), y(1)) + C(4)f(x(2), y(2)), (**)
for all x(i), y(i) is an element of X (i is an element of {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 (**). | pl_PL |
dc.language.iso | en | pl_PL |
dc.rights | Uznanie autorstwa 3.0 Polska | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/pl/ | * |
dc.subject | Linear equation | pl_PL |
dc.subject | Additive function | pl_PL |
dc.subject | Biadditive function | pl_PL |
dc.subject | Hamel basis | pl_PL |
dc.subject | Field ex-tension | pl_PL |
dc.subject | Algebraic dependence | pl_PL |
dc.title | On a general bilinear functional equation | pl_PL |
dc.type | info:eu-repo/semantics/article | pl_PL |
dc.relation.journal | Aequationes Mathematicae | pl_PL |
dc.identifier.doi | 10.1007/s00010-021-00819-5 | - |
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