Abstract
We prove in a general scheme of Banach spaces, that when a Jackson inequality of an appropriate order holds, Bernstein-type inequalities and their sharpenings in the sense of Stechkin and Nik'olskii are equivalent to one another.
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Translated from Matematicheskie Zametki, Vol. 17, No. 6, pp. 925–937, June, 1975.
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Scherer, K. Bernstein-type inequalities in a Banach space. Mathematical Notes of the Academy of Sciences of the USSR 17, 555–562 (1975). https://doi.org/10.1007/BF01442703
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DOI: https://doi.org/10.1007/BF01442703