Sharp Power Mean Bounds for Sándor Mean
We prove that the double inequality Mp(a,b)<X(a,b)<Mq(a,b) holds for all a,b>0 with a≠b if and only if p≤1/3 and q≥log 2/(1+log 2)=0.4093…, where X(a,b) and Mr(a,b) are the Sándor and rth power means of a and b, respectively.
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/172867 |
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| _version_ | 1832559909829345280 |
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| author | Yu-Ming Chu Zhen-Hang Yang Li-Min Wu |
| author_facet | Yu-Ming Chu Zhen-Hang Yang Li-Min Wu |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | We prove that the double inequality Mp(a,b)<X(a,b)<Mq(a,b) holds for all a,b>0 with a≠b if and only if p≤1/3 and q≥log 2/(1+log 2)=0.4093…, where X(a,b) and Mr(a,b) are the Sándor and rth power means of a and b, respectively. |
| format | Article |
| id | doaj-art-88ced14019844acc96557c31f6fb28b0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-88ced14019844acc96557c31f6fb28b02025-02-03T01:28:50ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/172867172867Sharp Power Mean Bounds for Sándor MeanYu-Ming Chu0Zhen-Hang Yang1Li-Min Wu2Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaDepartment of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaDepartment of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaWe prove that the double inequality Mp(a,b)<X(a,b)<Mq(a,b) holds for all a,b>0 with a≠b if and only if p≤1/3 and q≥log 2/(1+log 2)=0.4093…, where X(a,b) and Mr(a,b) are the Sándor and rth power means of a and b, respectively.http://dx.doi.org/10.1155/2015/172867 |
| spellingShingle | Yu-Ming Chu Zhen-Hang Yang Li-Min Wu Sharp Power Mean Bounds for Sándor Mean Abstract and Applied Analysis |
| title | Sharp Power Mean Bounds for Sándor Mean |
| title_full | Sharp Power Mean Bounds for Sándor Mean |
| title_fullStr | Sharp Power Mean Bounds for Sándor Mean |
| title_full_unstemmed | Sharp Power Mean Bounds for Sándor Mean |
| title_short | Sharp Power Mean Bounds for Sándor Mean |
| title_sort | sharp power mean bounds for sandor mean |
| url | http://dx.doi.org/10.1155/2015/172867 |
| work_keys_str_mv | AT yumingchu sharppowermeanboundsforsandormean AT zhenhangyang sharppowermeanboundsforsandormean AT liminwu sharppowermeanboundsforsandormean |