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arXiv · 1603.01338

Finding best possible constant for a polynomial inequality

Lu Yang·Ju Zhang
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Abstract

Given a multi-variant polynomial inequality with a parameter, how to find the best possible value of this parameter that satisfies the inequality? For instance, find the greatest number $k$ that satisfies $ a^3+b^3+c^3+ k(a^2b+b^2c+c^2a)-(k+1)(ab^2+bc^2+ca^2)\geq 0 $ for all nonnegative real numbers $ a,b,c $. Analogues problems often appeared in studies of inequalities and were dealt with by various methods. In this paper, a general algorithm is proposed for finding the required best possible constant. The algorithm can be easily implemented by computer algebra tools such as Maple.

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Lu Yang, Ju Zhang. 2016-03-04. Finding best possible constant for a polynomial inequality. https://arxiv.org/abs/1603.01338

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