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arXiv · 2311.17481

The Best Constant For Inequality Involving Sum Of The Reciprocals And Product Of Positive Numbers With Unit Sum

Yagub N. Aliyev
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Abstract

In the paper we study a special parameter containing algebraic inequality involving sum of reciprocals and product of positive real numbers whose sum is 1. We determine the best values of the parameter using a new optimization argument. In the case of three numbers the algebraic inequality have some interesting geometric applications involving a generalization of Euler's inequality about the ratio of radii of circumscribed and inscribed circles of a triangle.

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Yagub N. Aliyev. 2023-11-29. The Best Constant For Inequality Involving Sum Of The Reciprocals And Product Of Positive Numbers With Unit Sum. https://doi.org/10.1186/s13660-024-03107-3

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