Uniform approximation of some classes of linear positive operators expressed by series

Abstract

The paper deals with a general class of linear positive approximation processes designed using series. For continuous and bounded functions defined on unbounded interval we give rate of convergence in terms of the usual modulus of smoothness. The main goal is to identify functions for which these operators provide uniform approximation over unbounded intervals. Particular cases are delivered.

Keywords:

• Bohman–Korovkin theorem
• modulus of smoothness
• Szász operator
• Baskakov operator
• Mastroianni operator
• Jain operator
• Poisson distribution

AMS Subject Classifications:

• 41A35
• 26D15

Acknowledgements