A Functional Equation with Biadditive Functions

• Autorzy: Radosław Łukasik
• Języki publikacji: EN

Abstrakty

EN

Let S, H, X be groups. For two given biadditive functions A:S^2→X, B:H^2→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.(original abstract)

Słowa kluczowe

EN

Mathematics; Functions; Functional equation

PL

Matematyka; Funkcje; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2022
• Tom: 36 (2)
• Strony: 193--205

Twórcy

autor

Radosław Łukasik

• University of Silesia in Katowice Katowice, Poland

Bibliografia

• Chmielinski J., Orthogonality equation with two unknown functions, Aequationes Math. 90 (2016), no. 1, 11-23.
• Łukasik R., A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), no. 5, 961-965.
• Łukasik R., Some orthogonality equation with two functions, Miskolc Math. Notes 18 (2017), no. 2, 953-960.
• Łukasik R. and Wójcik P., Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), no. 3, 495-499.
• Łukasik R. and Wójcik P., Functions preserving the biadditivity, Results Math. 75 (2020), no. 3, Paper No. 82, 17 pp.
• Mlak W., Hilbert Spaces and Operator Theory, PWN-Polish Scientific Publishers, Warsaw, Kluwer Academic Publishers Group, Dordrecht, 1991.
• Sadr M.M., Decomposition of functions between Banach spaces in the orthogonality equation, Aequationes Math. 91 (2017), no. 4, 739-743.
• Wójcik P., On an orthogonality equation in normed spaces, Funct. Anal. Appl. 52 (2018), no. 3, 224-227.

Identyfikatory

DOI

10.2478/amsil-2022-0008