The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abstract spaces. Particular classes are also studied.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Korovkin theorem; King-type operator; rate of convergence; weighted modulus
O. Agratini, Linear operators that preserve some test functions, International Journal of Mathematics and Mathematical Sciences 2006, ID 94136, pp. 1-11, https://doi.org/10.1155/IJMMS/2006/94136
International Journal of Mathematics and Mathematical Sciences
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