Approximately generalized additive functions in several variables via fixed point method

	Approximately generalized additive functions in several variables via fixed point method
International Journal of Nonlinear Analysis and Applications
مقاله 17، دوره 7، شماره 1، 2016، صفحه 167-181 اصل مقاله (456.1 K)
شناسه دیجیتال (DOI): 10.22075/ijnaa.2015.304
نویسندگان
R. Farokhzad Rostami^* ¹؛ S.A.R. Hoseinioun²
¹Department of Mathematics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran
²Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
چکیده
In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equation \begin{align} &D_f(x_{1},.., x_{m}):= \sum^{m}_{k=2}(\sum^{k}_{i_{1}=2} \sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(\sum^{m}_{i=1, i\neq i_{1},...,i_{m-k+1} } x_{i}-\sum^{m-k+1}_{ r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{ i=1} x_{i}) -2^{m-1} f(x_{1})=0 \end{align} where $m \geq 2$ is an integer number.
کلیدواژه‌ها
Additive function؛ $p$-Banach spaces؛ Random normed spaces؛ Non-Archimedean spaces؛ Fixed point method؛ generalized Hyers-Ulam stability
آمار تعداد مشاهده مقاله: 18,982 تعداد دریافت فایل اصل مقاله: 13,981

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