Optimal Inequalities among Various Means of Two Arguments

We establish two optimal inequalities among power mean Mp(a,b)=(ap/2+bp/2)1/p, arithmetic mean A(a,b)=(a+b)/2, logarithmic mean L(a,b)=(a−b)/(log⁡a−log⁡b), and geometric mean G(a,b)=ab.

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Main Authors: Ming-yu Shi, Yu-ming Chu, Yue-ping Jiang
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2009/694394
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author Ming-yu Shi
Yu-ming Chu
Yue-ping Jiang
author_facet Ming-yu Shi
Yu-ming Chu
Yue-ping Jiang
author_sort Ming-yu Shi
collection DOAJ
description We establish two optimal inequalities among power mean Mp(a,b)=(ap/2+bp/2)1/p, arithmetic mean A(a,b)=(a+b)/2, logarithmic mean L(a,b)=(a−b)/(log⁡a−log⁡b), and geometric mean G(a,b)=ab.
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language English
publishDate 2009-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-4af959f3ca944009a6c7b3d4401e87162025-08-20T02:38:34ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/694394694394Optimal Inequalities among Various Means of Two ArgumentsMing-yu Shi0Yu-ming Chu1Yue-ping Jiang2College of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaDepartment of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaWe establish two optimal inequalities among power mean Mp(a,b)=(ap/2+bp/2)1/p, arithmetic mean A(a,b)=(a+b)/2, logarithmic mean L(a,b)=(a−b)/(log⁡a−log⁡b), and geometric mean G(a,b)=ab.http://dx.doi.org/10.1155/2009/694394
spellingShingle Ming-yu Shi
Yu-ming Chu
Yue-ping Jiang
Optimal Inequalities among Various Means of Two Arguments
Abstract and Applied Analysis
title Optimal Inequalities among Various Means of Two Arguments
title_full Optimal Inequalities among Various Means of Two Arguments
title_fullStr Optimal Inequalities among Various Means of Two Arguments
title_full_unstemmed Optimal Inequalities among Various Means of Two Arguments
title_short Optimal Inequalities among Various Means of Two Arguments
title_sort optimal inequalities among various means of two arguments
url http://dx.doi.org/10.1155/2009/694394
work_keys_str_mv AT mingyushi optimalinequalitiesamongvariousmeansoftwoarguments
AT yumingchu optimalinequalitiesamongvariousmeansoftwoarguments
AT yuepingjiang optimalinequalitiesamongvariousmeansoftwoarguments