Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means
We present the best possible parameters λ1,μ1∈R and λ2,μ2∈1/2,1 such that double inequalities λ1C(a,b)+1-λ1A(a,b)<T(a,b)<μ1C(a,b)+1-μ1A(a,b), Cλ2a+1-λ2b,λ2b+1-λ2a<T(a,b)<Cμ2a+1-μ2b,μ2b+1-μ2a hold for all a,b>0 with a≠b, where A(a,b)=(a+b)/2, C(a,b)=a3+b3/a2+b2 and T(a,b)=2∫0π/2a2cos2θ...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/452823 |
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| author | Wei-Mao Qian Ying-Qing Song Xiao-Hui Zhang Yu-Ming Chu |
| author_facet | Wei-Mao Qian Ying-Qing Song Xiao-Hui Zhang Yu-Ming Chu |
| author_sort | Wei-Mao Qian |
| collection | DOAJ |
| description | We present the best possible parameters λ1,μ1∈R and λ2,μ2∈1/2,1 such that double inequalities λ1C(a,b)+1-λ1A(a,b)<T(a,b)<μ1C(a,b)+1-μ1A(a,b), Cλ2a+1-λ2b,λ2b+1-λ2a<T(a,b)<Cμ2a+1-μ2b,μ2b+1-μ2a hold for all a,b>0 with a≠b, where A(a,b)=(a+b)/2, C(a,b)=a3+b3/a2+b2 and T(a,b)=2∫0π/2a2cos2θ+b2sin2θdθ/π are the arithmetic, second contraharmonic, and Toader means of a and b, respectively. |
| format | Article |
| id | doaj-art-66bdfc184d6a4ef18235110c320befc2 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-66bdfc184d6a4ef18235110c320befc22025-02-03T01:21:18ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/452823452823Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic MeansWei-Mao Qian0Ying-Qing Song1Xiao-Hui Zhang2Yu-Ming Chu3School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaWe present the best possible parameters λ1,μ1∈R and λ2,μ2∈1/2,1 such that double inequalities λ1C(a,b)+1-λ1A(a,b)<T(a,b)<μ1C(a,b)+1-μ1A(a,b), Cλ2a+1-λ2b,λ2b+1-λ2a<T(a,b)<Cμ2a+1-μ2b,μ2b+1-μ2a hold for all a,b>0 with a≠b, where A(a,b)=(a+b)/2, C(a,b)=a3+b3/a2+b2 and T(a,b)=2∫0π/2a2cos2θ+b2sin2θdθ/π are the arithmetic, second contraharmonic, and Toader means of a and b, respectively.http://dx.doi.org/10.1155/2015/452823 |
| spellingShingle | Wei-Mao Qian Ying-Qing Song Xiao-Hui Zhang Yu-Ming Chu Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means Journal of Function Spaces |
| title | Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means |
| title_full | Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means |
| title_fullStr | Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means |
| title_full_unstemmed | Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means |
| title_short | Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means |
| title_sort | sharp bounds for toader mean in terms of arithmetic and second contraharmonic means |
| url | http://dx.doi.org/10.1155/2015/452823 |
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