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The Scientific World Journal
Volume 2014 (2014), Article ID 174716, 17 pages
http://dx.doi.org/10.1155/2014/174716
Research Article

The Trigonometric Polynomial Like Bernstein Polynomial

School of Mathematics and Statistics, Central South University, Changsha 410083, China

Received 7 May 2014; Revised 6 August 2014; Accepted 6 August 2014; Published 27 August 2014

Academic Editor: Predrag S. Stanimirovic

Copyright © 2014 Xuli Han. 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

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given.