Optimal bounds for the sine and hyperbolic tangent means. IV
type: Item
instance of: scholarly article
title: Optimal bounds for the sine and hyperbolic tangent means. IV
zbMATH Open document ID: 1478.26025
author: Monika Nowicka
author: Alfred Witkowski
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2021-09-02T00:00:00Z
review text: The authors provide optimal bounds for the sine and hyperbolic tangent means in terms of various weighted means of the arithmetic and centroidal means. The sine and hyperbolic tangent means are defined, respectively, as follows: \[ M_{\sin} (x,y)= \left\{ \begin{array}{lcl} \frac{x-y}{2\sin\left(\frac{x-y}{x+y}\right)} & \mbox{if} & x\neq y \\ x & \mbox{if} & x=y \end{array}\right. \] and \[ M_{\tanh} (x,y)= \left\{ \begin{array}{lcl} \frac{x-y}{2\tanh\left(\frac{x-y}{x+y}\right)} & \mbox{if} & x\neq y \\ x & \mbox{if} & x=y \end{array}\right.. \] For Part I and II see [the authors, ``Optimal bounds for the sine and hyperbolic tangent means'', J. Math., Punjab Univ. 52, No. 5, 77--88 (2020); J. Appl. Anal. 27, No. 1, 65--72 (2021; Zbl 1473.26042)].
Mathematics Subject Classification ID: 26E60
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 7390106
zbMATH Keywords: sine mean
zbMATH Keywords: hyperbolic tangent mean
zbMATH Keywords: Seiffert function
reviewed by: Raghib Abu-Saris
MaRDI profile type: Publication
full work available at URL: s13398-021-01020-8
OpenAlex ID: W3137363594
Wikidata QID: Q115600892
cites work: Q4339229
cites work: Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
cites work: Bounds of the Neuman-Sándor mean using power and identric means
cites work: Sharp power mean bounds for Sándor mean
cites work: Sharp power mean bounds for two Sándor-Yang means
cites work: Bounds for the perimeter of an ellipse in terms of power means
cites work: The best bounds for Toader mean in terms of the centroidal and arithmetic means
cites work: A double inequality for bounding Toader mean by the centroidal mean
cites work: Q5513163
cites work: Sharp bounds for the Neuman-Sándor mean in terms of generalized logarithmic mean
cites work: Optimal bounds for the tangent and hyperbolic sine means II
cites work: Best possible bounds for Yang mean using generalized logarithmic mean
cites work: Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
cites work: Optimal two-parameter geometric and arithmetic mean bounds for the Sándor-Yang mean
cites work: Sharp bounds for the Toader-Qi mean in terms of harmonic and geometric means
cites work: Optimal bounds for Neuman mean using arithmetic and centroidal means
cites work: Sharp one-parameter geometric and quadratic means bounds for the Sándor-Yang means
cites work: On Seiffert-like means
cites work: Optimal inequalities between Neuman-Sándor, centroidal and harmonic means
cites work: Sharp bounds for the Sándor-Yang means in terms of arithmetic and contra-harmonic means
DOI: 10.1007/S13398-021-01020-8
description: scientific article; zbMATH DE number 7390106