پایداری هایزر-اولام φ-اشتقاق‌های همریختی در جبرهای باناخ مختلط

نوع مقاله : مقاله پژوهشی

نویسنده

دانشکده فنی مهندسی و علوم پایه، دانشگاه ولایت، ایرانشهر، ایران

10.22091/maa.2025.12962.1028

چکیده

فرض کنید $ \mathcal{A} $ یک جبر باناخ، $ x,y\in \mathcal{A} $ و $ \varphi,\psi: \mathcal{A}\rightarrow \mathcal{A} $ 
دو نگاشت جمعی باشند، در این مقاله دستگاه معادلات تابعی جمعی زیر را حل می‌کنیم 
$$\begin{cases} 
&2\varphi(x+y)=\psi(x-y),\\ 
&\psi(x+y)=2\varphi(y-x)+4\varphi(x). 
\end{cases}$$ 
همچنین، پایداری هایزر$ - $اولام دستگاه بالا در فضاهای باناخ مختلط را بررسی می‌کنیم. به‌علاوه، به کمک روش نقطه ثابت نشان می‌دهیم که پایداری هایزر$ - $اولام در جبرهای باناخ برقرار است. 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Hyers-Ulam stability of φ-hom-derivations in complex Banach algebras

نویسنده [English]

  • Mahnaz Rezaei
Department of Electrical and Electronic Engineering, Velayat University, Iranshahr, Iran
چکیده [English]

Let $ \mathcal{A} $ be a Banach algebra, $ x,y\in  \mathcal{A}  $ and $ \varphi,\psi: \mathcal{A} \rightarrow  \mathcal{A}  $ be two additive mappings. In this paper, we solve
    \begin{align*}
        \begin{cases}
            &2\varphi(x+y)=\psi(x-y),\\
            &\psi(x+y)=2\varphi(y-x)+4\varphi(x).
        \end{cases}
    \end{align*}
Also, we investigate the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability by fixed point method in Banach algebras.

کلیدواژه‌ها [English]

  • Additive mapping
  • Derivation
  • Fixed point method
  • Stability
  • System of additive functional equations
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دوره 2، شماره 2 - شماره پیاپی 3
در حال آماده سازی
دی 1403
صفحه 106-122
  • تاریخ دریافت: 25 مرداد 1403
  • تاریخ بازنگری: 02 آذر 1403
  • تاریخ پذیرش: 08 آذر 1403