对于具有负指数的广义幂平均不等式的更清晰的版本

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Mathematical Inequalities Pub Date : 2023-01-01 DOI:10.7153/jmi-2023-17-07

R. Tinaztepe, G. Tinaztepe, Zeynep Eken, Sevda Sezer, S. Kemali, Ilknur Yesilce Isik, S. S. Evcan

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引用次数: 1

摘要

。本文利用生成函数的最优性定理，重新定义了带负参数的广义幂平均不等式。最优性定理要求对指数的不同情况进行研究，并给出了在不等式存在的向量的邻域中不等式的一个重新定义。然后，通过适当选择参数，将这些局部不等式推广到所有正向量。并对部分结果进行了数值算例验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The sharper version for generalized power mean inequalities with negative exponent

. In this study, the generalized power mean inequalities with a negative parameter are re ﬁ ned using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a re ﬁ nement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exempli ﬁ ed by numerical calculations.

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来源期刊

Journal of Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.