一个新推广的Diaz-Metcalf不等式及其应用

A new generalized Diaz-Metcalf inequality and its applications

目的研究Diaz-Metcalf不等式的指数积分推广式,并在一定程度上得到了Kantorovich积分不等式和Pólya-Szeg积分不等式的推广形式。方法采用归纳类比思想方法得到了Diaz-Met-calf不等式的新推广式后,给出了简洁有趣的构造性方法的证明。结果表明运用新的Diaz-Metcalf积分不等式,能够明显地解决Kantorovich积分不等式和Pólya-Szeg积分不等式。结论通过归纳类比方法和构造性方法,确定了这两种方法是解决这一类积分不等式的较好手段。

Aim The exponential integral of Diaz Metcalf＇s inequality was studied to extend the general expression, and to obtain the Kantorovich integral inequality and Pólya-Szegoe integral inequality generalized form. Methods The induction and analogy were used to obtain a new general expression of Diaz-Metcalf＇s inequality and give a proof method of succinct and interesting structure. Results The Kantorovich integral inequality and Pólya-Szegoe integral inequality can obviously been solved to utilize the new Diaz-Metcalf integral inequality. Conclusion The induction and analogy, constructive methods are good methods of solving the integral inequalities.