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)/(loga−logb), and geometric mean G(a,b)=ab.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/694394 |
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| _version_ | 1850107534760738816 |
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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)/(loga−logb), and geometric mean G(a,b)=ab. |
| format | Article |
| id | doaj-art-4af959f3ca944009a6c7b3d4401e8716 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| 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)/(loga−logb), 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 |