Optimal bounds for two Seiffert-like means by arithmetic mean and harmonic mean

Zhu, Ling; Malešević, Branko

doi:10.1007/s13398-023-01387-w

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2023

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“…In 2020, Nowicka and Witkowski [30] provided the optimal weighted power mean bounds A p (A, G; w) (p = ±1, ±2) for the two new means M sinh and M tan . In another paper [31], the authors established the best weighted power mean bounds A p (A, H; w) (p = ±1, ±2) for M sinh and M tan , which were generalized by Zhu [32], Zhu and Malešević [33] as follows: the double inequalities…”

Section: Introductionmentioning

confidence: 99%

Sharp Power Mean Bounds for Two Seiffert-like Means

Yang,

Zhang

2023

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The mean is a subject of extensive study among scholars, and the pursuit of optimal power mean bounds is a highly active field. This article begins with a concise overview of recent advancements in this area, focusing specifically on Seiffert-like means. We establish sharp power mean bounds for two Seiffert-like means, including the introduction and establishment of the best asymmetric mean bounds for symmetric means. Additionally, we explore the practical applications of these findings by extending several intriguing chains of inequalities that involve more than ten means. This comprehensive analysis provides a deeper understanding of the relationships and properties of these means.

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