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<p/> <p>Gavrea and Ivan (2010) obtained an inequality for a continuous linear functional which annihilates all polynomials of degree at most <inline-formula> <graphic file="1029-242X-2011-179695-i1.gif"/></inline-formula> for some positive integer <inline-formula> <graphic file="1029-242X-2011-179695-i2.gif"/></inline-formula>. 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.</p>