<abstract xmlns="http://www.w3.org/1999/xhtml">

Let <italic>S</italic>, <italic>H</italic>, <italic>X</italic> be groups. For two given biadditive functions <italic>A</italic> : <italic>S</italic>2 → <italic>X</italic>, <italic>B</italic> : <italic>H</italic>2 → <italic>X</italic> and for two unknown mappings <italic>T</italic> : <italic>S</italic> → <italic>H</italic>, <italic>g</italic> : <italic>S</italic> → <italic>S</italic> we will study the functional equation
<italic>B</italic>(<italic>T</italic> (<italic>x</italic>), <italic>T</italic> (<italic>y</italic>)) = <italic>A</italic>(<italic>x, g</italic>(<italic>y</italic>)), <italic>x, y</italic> ∈ <italic>S,</italic>
which is a generalization of the orthogonality equation in Hilbert spaces.
</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.

A Functional Equation with Biadditive Functions

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A Functional Equation with Biadditive Functions"}

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...

A Functional Equation with Biadditive Functions

Published Online: May 02, 2022

Page range: 193 - 205

Received: Jan 12, 2022

Accepted: Apr 11, 2022

DOI: https://doi.org/10.2478/amsil-2022-0008

Keywords
biadditive function, orthogonality equation, isometry, adjoint operator

© 2022 Radosław Łukasik, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Functional Equation with Biadditive Functions

Published Online: May 02, 2022

Page range: 193 - 205

Received: Jan 12, 2022

Accepted: Apr 11, 2022

DOI: https://doi.org/10.2478/amsil-2022-0008

Keywordsbiadditive function, orthogonality equation, isometry, adjoint operator

© 2022 Radosław Łukasik, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
biadditive function, orthogonality equation, isometry, adjoint operator