Sharp power mean bounds for the lemniscate type means

In this paper, we present sharp power mean bounds for the so-called lemniscate type means, which were introduced by Neuman (Math Pannon 18(1):77–94, 2007). The obtained results measure what the distance is between the lemniscate-type means and power means. As applications, several new bounds for the...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 115; no. 4
Main Authors Zhao, Tie-Hong, Shen, Zhong-Hua, Chu, Yu-Ming
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
26E60
Lemniscate functions
Lemniscate mean
33E05
Power mean
Negative-positive series
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Summary:In this paper, we present sharp power mean bounds for the so-called lemniscate type means, which were introduced by Neuman (Math Pannon 18(1):77–94, 2007). The obtained results measure what the distance is between the lemniscate-type means and power means. As applications, several new bounds for the arc lemniscate functions are established.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01117-0