Journal of Applied Mathematics
Volume 2013 (2013), Article ID 421328, 10 pages
http://dx.doi.org/10.1155/2013/421328
Research Article

Positive Interpolation Operators with Exponential-Type Weights

Hee Sun Jung1 and Ryozi Sakai2

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

Received 26 December 2012; Accepted 7 March 2013

Academic Editor: Roberto Barrio

Copyright © 2013 Hee Sun Jung and Ryozi Sakai. 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.

Abstract

We consider positive operators on the real line with property of interpolation, and we show the weighted -convergence of the operators. We will construct an analogical operator of one which is studied by Knopfmacher (1986). Furthermore, we treat the Shepard-type interpolatory operator (cf. Xie et al. (1998)).