Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 725638, 20 pages
Research Article

On the Favard-Type Theorem and the Jackson-Type Theorem (II)

1Department of Mathematics Education, Sungkyunkwan University, Seoul 110-745, Republic of Korea
2Department of Mathematics, Meijo University, Nagoya 468-8502, Japan

Received 30 September 2011; Accepted 20 October 2011

Academic Editors: C. Lu and E. Yee

Copyright © 2011 Hee Sun Jung et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let R = ( βˆ’ ∞ , ∞ ) , and let 𝑄 ∈ β„‚ 1 ∢ ℝ β†’ [ 0 , ∞ ) be an even function. We consider the exponential weights 𝑀 ( π‘₯ ) = 𝑒 βˆ’ 𝑄 ( π‘₯ ) , π‘₯ ∈ ℝ . In this paper we investigate the relations between the Favard-type inequality and the Jackson-type inequality. We also discuss the equivalence of two K-functionals and the modulus of smoothness.