A functional equation with biadditive functions
Abstract
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.
Keywords
biadditive function; orthogonality equation; isometry; adjoint operator
References
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
https://orcid.org/0000-0001-9295-1476
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