Investigation of the Stability via Shadowing Property
نویسندگان
چکیده
The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: 4n−2Cn/2−1rf ∑n j 1 xj/r n ∑ ik∈{0,1}, ∑n k 1 ik n/2 r2f ∑n i 1 −1 ik xi/r 4n·n−2Cn/2−1 ∑n i 1 f xi , where n ≥ 2, r ∈ R r2 / n and f is a mapping. And we prove that the even mapping which satisfies the above equation is quadratic and also the Hyers-Ulam stability of the functional equation in Banach spaces.
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