A Functional Equation with Biadditive Functions

Łukasik, Radosław

doi:10.2478/amsil-2022-0008

.blurhash-client-img { display: none !important; }

A Functional Equation with Biadditive Functions

Annales Mathematicae Silesianae

Volume 36 (2022): Issue 2 (September 2022)

By: Radosław Łukasik

Open Access

|May 2022

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.

References

[1] J. Chmieliński, Orthogonality equation with two unknown functions, Aequationes Math. 90 (2016), no. 1, 11–23.
Search in Google Scholar Back to article
[2] R. Łukasik, A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), no. 5, 961–965.
Search in Google Scholar Back to article
[3] R. Łukasik, Some orthogonality equation with two functions, Miskolc Math. Notes 18 (2017), no. 2, 953–960.
Search in Google Scholar Back to article
[4] R. Łukasik and P. Wójcik, Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), no. 3, 495–499.
Search in Google Scholar Back to article
[5] R. Łukasik and P. Wójcik, Functions preserving the biadditivity, Results Math. 75 (2020), no. 3, Paper No. 82, 17 pp.10.1007/s00025-020-01206-3
Search in Google Scholar Back to article
[6] W. Mlak, Hilbert Spaces and Operator Theory, PWN–Polish Scientific Publishers, Warsaw, Kluwer Academic Publishers Group, Dordrecht, 1991.
Search in Google Scholar Back to article
[7] M.M. Sadr, Decomposition of functions between Banach spaces in the orthogonality equation, Aequationes Math. 91 (2017), no. 4, 739–743.
Search in Google Scholar Back to article
[8] P. Wójcik, On an orthogonality equation in normed spaces, Funct. Anal. Appl. 52 (2018), no. 3, 224–227.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/amsil-2022-0008 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 193 - 205

Submitted on: Jan 12, 2022

Accepted on: Apr 11, 2022

Published on: May 2, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

biadditive function,

orthogonality equation,

Related subjects:

© 2022 Radosław Łukasik, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Previous article Volume 36 (2022): Issue 2 (September 2022)Next article