Journal of Inequalities and Applications
Volume 2 (1998), Issue 4, Pages 297-306
doi:10.1155/S1025583498000198
Abstract
This note is concerned with a comparison of the approximation-theoretical behaviour of trigonometric convolution processes and their discrete analogues. To be more specific, for continuous functions it is a well-known fact that under suitable conditions the relevant uniform errors are indeed equivalent, apart from constants. It is the purpose of this note to extend the matter to the frame of Riemann integrable functions. To establish the
comparison for the corresponding Riemann errors, essential use is made of appropriate stability inequalities.