Abstract
We investigate one inequality in approximation theory and obtain necessary and sufficient conditions for the validity of this inequality. We present several examples demonstrating that the results obtained are unimprovable.
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REFERENCES
N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).
V. F. Storchai, “Exact estimates for the norms of differentiable periodic functions in the metric of L2,” Ukr. Mat. Zh., 25, No. 6, 835–840 (1973).
O. V. Tchernitskaya, “Approximation of continuous functions by step functions in integral metrics,” East J. Approxim., 5, No. 4, 403–418 (1999).
O. V. Chernitskaya, “On the approximation of continuous functions by piecewise-constant functions in integral metrics,” Visn. Dnipropetr. Univ., Mat., Issue 4, 128–138 (1998).
O. V. Chernyts'ka, Approximation of Functions of the Classes H ω ωin Spaces with Integral Metric [in Ukrainian], Author's Candidate-Degree Thesis (Physics and Mathematics), Dnepropetrovsk (2001).
I. P. Natanson, Theory of Functions of Real Variables [in Russian], Nauka, Moscow (1974).
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Leonchik, E.Y. On One Inequality in Approximation Theory. Ukrainian Mathematical Journal 55, 1899–1906 (2003). https://doi.org/10.1023/B:UKMA.0000027050.30860.49
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DOI: https://doi.org/10.1023/B:UKMA.0000027050.30860.49