Bound on deviations of continuous periodic functions from their de la Vallée-Poussin sums
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Abstract
We show that for every continuous function with period 2Μ, where C is an absolute constant and 0 ≤ m ≤ n, and we then apply this bound.
$$|f(x) - V_{n,m} (f,x)| \leqslant \frac{C}{{m + 1}}\sum\nolimits_{h = n - m}^n {E_k [1 + In\left( {\frac{{n - m}}{{h - n + m + 1}}} \right)],}$$
Keywords
Continuous Function Periodic Function Absolute Constant Continuous Periodic Function
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