On the hyperstability of <em>(m,n)</em>-derivations


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	*On the hyperstability of (m,n)-derivations*


	Fixed Point Theory, Volume 18, No. 2, 2017, 641-650, June 1st, 2017 DOI: 10.24193/fpt-ro.2017.2.51 Authors: Hamid Khodaei Abstract: Let $\mathcal{A}$ be a unital algebra, let $\mathcal{X}$ be a unital $\mathcal{A}$ -module for which $\mathcal{X}_{\rho}$ is a ρ-complete modular space and let $f:\mathcal{A}\to\mathcal{X}_{\rho}$ be a mapping. We present some observations concerning hyperstability of the following functional equations $\mu f\left(\frac{x + y}{2}\right) + \mu f\left(\frac{x-y}{2}\right)=f(\mu x),\hspace{.5cm}(m + n)f(xy)=2mx\cdot f(y) + 2ny\cdot f(x)$ for all $x,y\in \mathcal{A}$ and all $\mu\in T_{1/n_0}=\{e^{i\theta};~ 0\leq\theta\leq2\pi/n_0\}$ , where m, n ≥0 with m + n ≠ 0 are fixed integers. Key Words and Phrases: Approximately (m,n)-derivation, fixed point, hyperstability, modular space, unital algebra. 2010 Mathematics Subject Classification: 39B52, 39B82, 47B47, 47H09, 47H10. Published on-line: June 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents