The Jackson theorem for the smoothness modulus determined by nonsymmetric generalized shift operator. (English. Russian original) Zbl 0998.41017

Mosc. Univ. Math. Bull. 55, No. 3, 6-14 (2000); translation from Vestn. Mosk. Univ., Ser. I 2000, No. 3, 7-15 (2000).
The author considers a class of nonsymmetric operators of generalized shift. For each operator the generalized smoothness moduli are introduced. The Jackson theorem is proved for the smoothness module as well as the converse theorem.


41A36 Approximation by positive operators
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiń≠-type inequalities)