Finding best possible constant for a polynomial inequality

03/04/2016

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by   Lu Yang, et al.

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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)≥ 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.