Abstract
For a function ƒ continuous on [0, 1] and satisfying the equalities \(f(0) = f\left( {\frac{1}{3}} \right) = f\left( {\frac{2}{3}} \right) = f(1) = 0,\) we prove that \(|f(x)| \le 2\omega _4 \left( {\frac{1}{4},f} \right),{\rm{ }}x \in [0,1],\) where ω4(t,ƒ) is the fourth modulus of smoothness of the function ƒ.
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References
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 732–734, May, 1998.
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Danilenko, I.G. On the Sendov problem on the Whitney interpolation constant. Ukr Math J 50, 831–833 (1998). https://doi.org/10.1007/BF02514335
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DOI: https://doi.org/10.1007/BF02514335