<abstract xmlns="http://www.w3.org/1999/xhtml">
Let <italic>X </italic>be an Abelian group, <italic>Y </italic>be a commutative monoid, <italic>K </italic>⊂<italic>Y </italic> be a submonoid and <italic>F </italic>: <italic>X → </italic>2<italic>Y </italic><italic>\ </italic>{∅} be a set-valued map. Under some additional assumptions on ideals <italic>ℐ</italic>1 in <italic>X </italic>and <italic>ℐ</italic>2 in <italic>X</italic>2, we prove that if <italic>F </italic>is <italic>ℐ</italic>2-almost everywhere <italic>K</italic>-additive, then there exists a unique up to <italic>K K</italic>-additive set-valued map <italic>G </italic>: <italic>X → </italic>2<italic>Y </italic><italic>\</italic>{∅} such that <italic>F </italic>= <italic>G ℐ</italic>1-almost everywhere in <italic>X</italic>. Our considerations refers to the well known de Bruijn’s result [1].
</abstract>

Let X be an Abelian group, Y be a commutative monoid, K ⊂Y  be a submonoid and F : X → 2Y \ {∅} be a set-valued map. Under some additional assumptions on ideals ℐ1 in X and ℐ2 in X2, we prove that if F is ℐ2-almost everywhere K-additive, then there exists a unique up to K K-additive set-valued map G : X → 2Y \{∅} such that F = G ℐ1-almost everywhere in X. Our considerations refers to the well known de Bruijn’s result [1].

On Almost Everywhere <italic>K</italic>-Additive Set-Valued Maps

Annales Mathematicae Silesianae

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On Almost Everywhere -Additive Set-Valued Maps

{"article-title":{"italic":"K","content":["On Almost Everywhere","-Additive Set-Valued Maps"]}}

Let X be an Abelian group, Y be a commutative monoid, K ⊂Y  be a submonoid and F : X → 2Y \ {∅} be a set-valued map. Under some additional assumptions on...

On Almost Everywhere K-Additive Set-Valued Maps

Published Online: Dec 13, 2023

Page range: 29 - 36

Received: Jun 27, 2023

Accepted: Dec 05, 2023

DOI: https://doi.org/10.2478/amsil-2023-0025

Keywords
monoid, Abelian group, -additive set-valued map, ideal, almost everywhere

© 2023 Eliza Jabłońska, published by Sciendo

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

On Almost Everywhere K-Additive Set-Valued Maps

Published Online: Dec 13, 2023

Page range: 29 - 36

Received: Jun 27, 2023

Accepted: Dec 05, 2023

DOI: https://doi.org/10.2478/amsil-2023-0025

Keywordsmonoid, Abelian group, -additive set-valued map, ideal, almost everywhere

© 2023 Eliza Jabłońska, published by Sciendo

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

Keywords
monoid, Abelian group, -additive set-valued map, ideal, almost everywhere