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.