Solution of some irregular functional equations and their stability

Journal of Linear and Topological Algebra

دوره 11، شماره 04، اسفند 2022، صفحه 271-277   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.699062

نویسندگان

Y. Sayyari^{* 1}؛ M. Dehghanian¹؛ Sh. Nasiri²

¹Department of Mathematics, Sirjan University of Technology, P. O. Box 78137-33385, Sirjan, Iran

²Department of Computer Engineering, Sirjan University of Technology P. O. Box 78137-33385, Sirjan, Iran

چکیده

‎In this note‎, ‎we study the following functional equations‎:
‎\begin{align*}‎
‎&L(L(p ,r)+L(‎q‎,r)+p + q ,r)+L(L( p, r)+ p , r)+L(q, r )=0,\\‎
‎&L(L( p , r )+ p + q+e, r )+L( p, r)=L( p + q , r )+ p L(q , r)
‎\end{align*}‎
‎and‎ ‎$‎L( p , q )=L(\zeta  p , q), \vert \zeta\vert <1‎$,‎ without any regularity assumption for all $ p , q , r \in A$, where $L:A^2\rightarrow A$ is defined by ‎$‎L( p ,  q ):=g( p + q )-g( p  )-g( q )‎$‎ for all $ p , q\in A$. Also, we find general solutions of the above functional equations on algebras, unital algebras and real numbers, respectively. Finally, we investigate the  stability of those functional equations in algebras and unital algebras, respectively.

کلیدواژه‌ها

Additive functional equation؛ unital algebra؛ Hyers-Ulam stability

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