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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 824058, 5 pages
http://dx.doi.org/10.1155/2013/824058
Research Article

Optimal Simultaneous Approximation via -Summability

1Departamento de Matemáticas, I.E.S. Virgen del Carmen, 23008 Jaén, Spain
2Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas s/n., 23071 Jaén, Spain

Received 22 May 2013; Accepted 15 August 2013

Academic Editor: Zhongxiao Jia

Copyright © 2013 Francisco Aguilera 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.

Abstract

We present optimal convergence results for the mth derivative of a function by sequences of linear operators. The usual convergence is replaced by -summability, with being a sequence of infinite matrices with nonnegative real entries, and the operators are assumed to be m-convex. Saturation results for nonconvergent but almost convergent sequences of operators are stated as corollaries.