Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 179695, 9 pages
doi:10.1155/2011/179695
Research Article

A New Proof of Inequality for Continuous Linear Functionals

Feng Cui and Shijun Yang

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received 23 January 2011; Accepted 2 March 2011

Academic Editor: Andrei Volodin

Copyright © 2011 Feng Cui and Shijun Yang. 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

Gavrea and Ivan (2010) obtained an inequality for a continuous linear functional which annihilates all polynomials of degree at most 𝑘 − 1 for some positive integer 𝑘 . In this paper, a new functional proof by Riesz representation theorem is provided. Related results and further applications of the inequality are also brought together.