Sharp bounds for the Toader mean in terms of arithmetic and geometric means
type: Item
instance of: scholarly article
title: Sharp bounds for the Toader mean in terms of arithmetic and geometric means
zbMATH Open document ID: 1475.26032
author: Zhen-Hang Yang
author: Jingfeng Tian
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2021-05-17T00:00:00Z
review text: The authors offer sharp lower and upper bounds for a mean of two arguments considered by \textit{G. Toader} [J. Math. Anal. Appl. 218, No. 2, 358--368 (1998; Zbl 0892.26015)], in terms of the arithmetic and geometric mean. In the proofs, the well-known connection between the Toader mean and the complete elliptic integral of second type is used. A basic method of proof is the recurrence method combined with the classical result of \textit{M. Biernacki} and \textit{J. Krzyz} [Ann. Univ. Mariae Curie-Skłodowska, Sect. A 9, 135--147 (1957; Zbl 0078.26402)] on the monotonicity of the ratio of power series. Another tool is a monotonicity criteria due to \textit{Z.-H. Yang} et al. [J. Math. Anal. Appl. 428, No. 1, 587--604 (2015; Zbl 1321.26019)].
reviewed by: József Sándor
Mathematics Subject Classification ID: 26E60
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 7348577
zbMATH Keywords: Toader mean
zbMATH Keywords: complete elliptic integral of second type
zbMATH Keywords: monotonicity
zbMATH Keywords: inequalities for means
MaRDI profile type: Publication
full work available at URL: s13398-021-01040-4
OpenAlex ID: W3151163838
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DOI: 10.1007/S13398-021-01040-4