A functional equation with biadditive functions

Radosław Łukasik

Published: 2022-05-02

Vol. 36 No. 2 (2022)

A functional equation with biadditive functions

Radosław Łukasik

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

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Łukasik, R. (2022). A functional equation with biadditive functions. Annales Mathematicae Silesianae, 36(2), 193–205. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13591

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Vol. 36 No. 2 (2022)
Published: 2022-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

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