A Sharp Lower Bound for Toader-Qi Mean with Applications
We prove that the inequality TQ(a,b)>Lp(a,b) holds for all a,b>0 with a≠b if and only if p≤3/2, where TQ(a,b)=2/π∫0π/2acos2θbsin2θdθ, Lp(a,b)=[(bp-ap)/(p(b-a))]1/p (p≠0), and L0(a,b)=ab are, respectively, the Toader-Qi and p-order logarithmic means of a and b. As applications, we find two fin...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/4165601 |
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| author | Zhen-Hang Yang Yu-Ming Chu |
| author_facet | Zhen-Hang Yang Yu-Ming Chu |
| author_sort | Zhen-Hang Yang |
| collection | DOAJ |
| description | We prove that the inequality TQ(a,b)>Lp(a,b) holds for all a,b>0 with a≠b if and only if p≤3/2, where TQ(a,b)=2/π∫0π/2acos2θbsin2θdθ, Lp(a,b)=[(bp-ap)/(p(b-a))]1/p (p≠0), and L0(a,b)=ab are, respectively, the Toader-Qi and p-order logarithmic means of a and b. As applications, we find two fine inequalities chains for certain bivariate means. |
| format | Article |
| id | doaj-art-bb93b9ac2e40459385b9fe8e768961ee |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-bb93b9ac2e40459385b9fe8e768961ee2025-02-03T06:42:03ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/41656014165601A Sharp Lower Bound for Toader-Qi Mean with ApplicationsZhen-Hang Yang0Yu-Ming Chu1School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaWe prove that the inequality TQ(a,b)>Lp(a,b) holds for all a,b>0 with a≠b if and only if p≤3/2, where TQ(a,b)=2/π∫0π/2acos2θbsin2θdθ, Lp(a,b)=[(bp-ap)/(p(b-a))]1/p (p≠0), and L0(a,b)=ab are, respectively, the Toader-Qi and p-order logarithmic means of a and b. As applications, we find two fine inequalities chains for certain bivariate means.http://dx.doi.org/10.1155/2016/4165601 |
| spellingShingle | Zhen-Hang Yang Yu-Ming Chu A Sharp Lower Bound for Toader-Qi Mean with Applications Journal of Function Spaces |
| title | A Sharp Lower Bound for Toader-Qi Mean with Applications |
| title_full | A Sharp Lower Bound for Toader-Qi Mean with Applications |
| title_fullStr | A Sharp Lower Bound for Toader-Qi Mean with Applications |
| title_full_unstemmed | A Sharp Lower Bound for Toader-Qi Mean with Applications |
| title_short | A Sharp Lower Bound for Toader-Qi Mean with Applications |
| title_sort | sharp lower bound for toader qi mean with applications |
| url | http://dx.doi.org/10.1155/2016/4165601 |
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