On the stability of the equation stemming from Lagrange MVT
نویسندگان
چکیده
The stability behaviour of the functional equation F (y) − F (x) = (y − x)f ( (x+ y)/2 ) is studied. It is proved that this equation is superstable i.e. if f, F satisfy ∣∣F (y) − F (x)(y − x)f((x + y)/2)∣∣ ≤ ε then f satisfies this equation (with some F ). In order to obtain this result the equation h∆hf(x) = 0 is considered and it is proved that also this equation is superstable.
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 24 شماره
صفحات -
تاریخ انتشار 2011