On an Extension of Shapiro's Cyclic Inequality
© N. M. Tuan and L. Q. Thuong. 2009
Received: 21 August 2009
Accepted: 13 October 2009
Published: 15 October 2009
We prove an interesting extension of the Shapiro's cyclic inequality for four and five variables and formulate a generalization of the well-known Shapiro's cyclic inequality. The method used in the proofs of the theorems in the paper concerns the positive quadratic forms.
In this note, by studying (1.2) in the case , we show that it is true when , and false when . Moreover, we give a sufficient condition of , under which (1.2) is true in the case . It is worth saying that if , then (1.2) is false for every even . Two open questions are discussed at the end of this paper.
2. Main Result
The theorem is proved.
This work is supported partially by Vietnam National Foundation for Science and Technology Development.
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