Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means
We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b)+(1-α1)H(a,b)<A(a,b)<β1M(a,b)+ (1-β1)H(a,b), α2M(a,b)+(1-α2) H-(a,b) < A(a,b)<β2M(a,b)+(1-β2)H-(a,b), and α3M(a,b)+(1-α3)He(a,b)< A(a,b)<β3M (a,b)+(1-β3)He(...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/582504 |
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| author | Fan Zhang Yu-Ming Chu Wei-Mao Qian |
| author_facet | Fan Zhang Yu-Ming Chu Wei-Mao Qian |
| author_sort | Fan Zhang |
| collection | DOAJ |
| description | We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b)+(1-α1)H(a,b)<A(a,b)<β1M(a,b)+ (1-β1)H(a,b), α2M(a,b)+(1-α2) H-(a,b) < A(a,b)<β2M(a,b)+(1-β2)H-(a,b), and α3M(a,b)+(1-α3)He(a,b)< A(a,b)<β3M (a,b)+(1-β3)He(a,b) hold for all a,b>0 with a≠b, where M(a,b), A(a,b), He(a,b), H(a,b) and H-(a,b) denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively. |
| format | Article |
| id | doaj-art-2ddcdaa466bc48ef86caa2cc97f59c75 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2ddcdaa466bc48ef86caa2cc97f59c752025-08-20T03:20:26ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/582504582504Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate MeansFan Zhang0Yu-Ming Chu1Wei-Mao Qian2School of Architecture Engineering, Huzhou Vocational & Technical College, Huzhou 313000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaDepartment of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, ChinaWe present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b)+(1-α1)H(a,b)<A(a,b)<β1M(a,b)+ (1-β1)H(a,b), α2M(a,b)+(1-α2) H-(a,b) < A(a,b)<β2M(a,b)+(1-β2)H-(a,b), and α3M(a,b)+(1-α3)He(a,b)< A(a,b)<β3M (a,b)+(1-β3)He(a,b) hold for all a,b>0 with a≠b, where M(a,b), A(a,b), He(a,b), H(a,b) and H-(a,b) denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively.http://dx.doi.org/10.1155/2013/582504 |
| spellingShingle | Fan Zhang Yu-Ming Chu Wei-Mao Qian Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means Journal of Applied Mathematics |
| title | Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means |
| title_full | Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means |
| title_fullStr | Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means |
| title_full_unstemmed | Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means |
| title_short | Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means |
| title_sort | bounds for the arithmetic mean in terms of the neuman sandor and other bivariate means |
| url | http://dx.doi.org/10.1155/2013/582504 |
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