On converse approximation theorems ✩

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 (Ln)n 1, Ln :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 Szász– Mirakjan type operators.  2005 Elsevier Inc. All rights reserved