Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean-Reference-Cited by-同舟云学术

Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean

Published:2013 Issue: Volume:2013 Page:1-4
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Matejíčka Ladislav¹^ORCID

Affiliation:

1. Faculty of Industrial Technologies in Púchov, Trenčín University of Alexander Dubček in Trenčín, I. Krasku 491/30, 02001 Púchov, Slovakia

Abstract

Optimal bounds for the weighted geometric mean of the first Seiffert and logarithmic means by weighted generalized Heronian mean are proved. We answer the question: for what the greatest value and the least value such that the double inequality, , holds for all with are. Here, and denote the first Seiffert, logarithmic, and weighted generalized Heronian means of two positive numbers and respectively.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2013/721539.pdf

Reference11 articles.

1. Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean

2. An Optimal Double Inequality between Power-Type Heron and Seiffert Means

3. An Optimal Double Inequality between Seiffert and Geometric Means

4. Sharp bounds by the power mean for the generalized Heronian mean

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