International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 545780, 8 pages
http://dx.doi.org/10.1155/2011/545780
Research Article

A Moment Problem for Discrete Nonpositive Measures on a Finite Interval

M. U. Kalmykov1 and S. P. Sidorov2

1Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410060, Russia
2School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge UB8 3PH, UK

Received 29 December 2010; Revised 16 March 2011; Accepted 22 March 2011

Academic Editor: Palle E. Jorgensen

Copyright © 2011 M. U. Kalmykov and S. P. Sidorov. 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 will estimate the upper and the lower bounds of the integral ∫ 1 0 Ω ( 𝑡 ) 𝑑 𝜇 ( 𝑡 ) , where 𝜇 runs over all discrete measures, positive on some cones of generalized convex functions, and satisfying certain moment conditions with respect to a given Chebyshev system. Then we apply these estimations to find the error of optimal shape-preserving interpolation.