Stability of partially pexiderized exponential-radical functional equation
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Let $\mathbb R$ be the set of real numbers, $f,g:\mathbb R \to \mathbb R$ and $\epsilon \ge 0$. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation \begin{equation} f\left(\sqrt[N]{x^N+y^N}\right)=f(x)g(y) \nonumber \end{equation} for all $x, y\in \mathbb R$, i.e., we investigate the functional inequality \begin{equation} \left|f\left(\sqrt[N]{x^N+y^N}\right)-f(x)g(y)\right| \leq \epsilon \nonumber \end{equation} for all $x, y\in \mathbb R$.
Abstract
Let $\mathbb R$ be the set of real numbers, $f,g:\mathbb R \to \mathbb R$ and $\epsilon \ge 0$. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation \begin{equation} f\left(\sqrt[N]{x^N+y^N}\right)=f(x)g(y) \nonumber \end{equation} for all $x, y\in \mathbb R$, i.e., we investigate the functional inequality \begin{equation} \left|f\left(\sqrt[N]{x^N+y^N}\right)-f(x)g(y)\right| \leq \epsilon \nonumber \end{equation} for all $x, y\in \mathbb R$.
참고문헌 (9)
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