Language:
EN
| Published:
30-09-1994
|
Abstract
| pp. 127-140
We consider a class of approximate solutions of the generalized orthogonality equation in ℝn (n≥2). We prove that this class coincides with the class of solutions of the equation, i.e., the superstability of the generalized orthogonality equation holds.
Language:
EN
| Published:
02-05-2022
|
Abstract
| pp. 193-205
Let S, H, X be groups. For two given biadditive functions A:S2→X, B:H2→X and for two unknown mappings T:S→H, g:S→S we will study the functional equation B(T(x),T(y)) = A(x,g(y)), x,y∈S, which is a generalization of the orthogonality equation in Hilbert spaces.
Language:
EN
| Published:
30-01-2003
|
Abstract
| pp. 65-77
Let X, Y be real linear spaces. We are looking for a function G : X2→ℝ such that the equation f(x+y) = G(x,y)[f(x)+f(y)] is equivalent to the orthogonal Cauchy equation x⟂y ⇒ f(x+y)=f(x)+f(y). Several kinds of orthogonalities are considered. The quotient ‖(x-y)/(x+y)‖ closely connected with the James orthogonality plays here a distinguished role. Similar problems are considered for the Ptolemaic equation x⟂y ⇒ f(x+y)f(x-y) = f(x)2+f(y)2. As a result a characterization of inner product spaces is obtained.
2003-01-30
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