Ulam stability of hom-ders in fuzzy Banach algebras

• DOI: 10.3934/math.2022907
• Publication Date: 2022-07-08T10:41:10Z
• Authors: Araya Kheawborisut; Siriluk Paokanta; Jedsada Senasukh; Choonkil Park
• Keywords: Artificial intelligence; 01 natural sciences; ulam stability result; Banach algebra; Machine learning; QA1-939; FOS: Mathematics; 0101 mathematics; Stability (learning theory); fixed point method; Banach space; Applied Mathematics; Pure mathematics; fuzzy banach algebra; Stability of Functional Equations in Mathematical Analysis; Hyers-Ulam Stability; Discrete mathematics; Computer science; Fixed Point Approach; Programming language; Fuzzy logic; Combinatorics; Physical Sciences; Integer (computer science); hom-der; Fuzzy Stability; Mathematics

<abstract><p>This paper aims to investigate a new type of derivations in a fuzzy Banach algebra. Moreover, by using the fixed point method, we obtain some stability results of the hom-der in fuzzy Banach algebras associated with the functional equation</p>

<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ f(x+{\textbf{k}}y) = f(x)+{\textbf{k}}f(y) $\end{document} </tex-math></disp-formula></p>

<p>where $ {\textbf{k}} $ is a fixed positive integer greater than $ 1 $.</p></abstract>