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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References

J. Chmielinski, Orthogonality equation with two unknown functions, Aequationes Math. 90 (2016), no. 1, 11–23.
Google Scholar

R. Łukasik, A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), no. 5, 961–965.
Google Scholar

R. Łukasik, Some orthogonality equation with two functions, Miskolc Math. Notes 18 (2017), no. 2, 953–960.
Google Scholar

R. Łukasik and P. Wójcik, Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), no. 3, 495–499.
Google Scholar

R. Łukasik and P. Wójcik, Functions preserving the biadditivity, Results Math. 75 (2020), no. 3, Paper No. 82, 17 pp.
Google Scholar

W. Mlak, Hilbert Spaces and Operator Theory, PWN–Polish Scientific Publishers, Warsaw, Kluwer Academic Publishers Group, Dordrecht, 1991.
Google Scholar

M.M. Sadr, Decomposition of functions between Banach spaces in the orthogonality equation, Aequationes Math. 91 (2017), no. 4, 739–743.
Google Scholar

P. Wójcik, On an orthogonality equation in normed spaces, Funct. Anal. Appl. 52 (2018), no. 3, 224–227.
Google Scholar

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

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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