On converse approximation theorems

By Z. Finta. 2005

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Abstract We establish sufficient conditions for obtaining a strong converse inequality of type B in terms of a unified K-functional for a sequence of linear positive operators ( L n ) n ⩾ 1 , L n : C [ 0 , ∞ ) → C [ 0 , ∞ ) . This K-functional, introduced by Guo et al. (see, e.g., [S. Guo, Q. Qi, Strong converse inequalities for Baskakov operators, J. Approx. Theory 124 (2003) 219–231]), will be considered for more general weight functions. As applications we investigate the situation for Baskakov type operators and Szasz–Mirakjan type operators.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

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