Sharp Geometric Mean Bounds for Neuman Means
We find the best possible constants α1,α2,β1,β2∈[0,1/2] and α3,α4,β3,β4∈[1/2,1] such that the double inequalities G(α1a+(1-α1)b,α1b + (1-α1)a)<NAG(a,b)<G(β1a + (1-β1)b,β1b+(1-β1)a),G(α2a+(1-α2)b,α2b + (1-α2)a)<NGA(a,b)<G(β2a + (1-β2)b,β2b+(1-β2)a),Q(α3a+(1-α3)b,α3b + (1-α3)a)<NQA(a,b)...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/949815 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849405913856737280 |
|---|---|
| author | Yan Zhang Yu-Ming Chu Yun-Liang Jiang |
| author_facet | Yan Zhang Yu-Ming Chu Yun-Liang Jiang |
| author_sort | Yan Zhang |
| collection | DOAJ |
| description | We find the best possible constants α1,α2,β1,β2∈[0,1/2] and α3,α4,β3,β4∈[1/2,1] such that the double inequalities G(α1a+(1-α1)b,α1b + (1-α1)a)<NAG(a,b)<G(β1a + (1-β1)b,β1b+(1-β1)a),G(α2a+(1-α2)b,α2b + (1-α2)a)<NGA(a,b)<G(β2a + (1-β2)b,β2b+(1-β2)a),Q(α3a+(1-α3)b,α3b + (1-α3)a)<NQA(a,b)<Q(β3a + (1-β3)b,β3b+(1-β3)a),Q(α4a+(1-α4)b,α4b + (1-α4)a)<NAQ(a,b)<Q(β4a + (1-β4)b,β4b+(1-β4)a) hold for all a,b>0 with a≠b, where G, A, and Q are, respectively, the geometric, arithmetic, and quadratic means and NAG, NGA, NQA, and NAQ are the Neuman means. |
| format | Article |
| id | doaj-art-52b059c931344eb4bee2e656d3cf0f7a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-52b059c931344eb4bee2e656d3cf0f7a2025-08-20T03:36:34ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/949815949815Sharp Geometric Mean Bounds for Neuman MeansYan Zhang0Yu-Ming Chu1Yun-Liang Jiang2School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaSchool of Information Engineering, Huzhou Teachers College, Huzhou 313000, ChinaWe find the best possible constants α1,α2,β1,β2∈[0,1/2] and α3,α4,β3,β4∈[1/2,1] such that the double inequalities G(α1a+(1-α1)b,α1b + (1-α1)a)<NAG(a,b)<G(β1a + (1-β1)b,β1b+(1-β1)a),G(α2a+(1-α2)b,α2b + (1-α2)a)<NGA(a,b)<G(β2a + (1-β2)b,β2b+(1-β2)a),Q(α3a+(1-α3)b,α3b + (1-α3)a)<NQA(a,b)<Q(β3a + (1-β3)b,β3b+(1-β3)a),Q(α4a+(1-α4)b,α4b + (1-α4)a)<NAQ(a,b)<Q(β4a + (1-β4)b,β4b+(1-β4)a) hold for all a,b>0 with a≠b, where G, A, and Q are, respectively, the geometric, arithmetic, and quadratic means and NAG, NGA, NQA, and NAQ are the Neuman means.http://dx.doi.org/10.1155/2014/949815 |
| spellingShingle | Yan Zhang Yu-Ming Chu Yun-Liang Jiang Sharp Geometric Mean Bounds for Neuman Means Abstract and Applied Analysis |
| title | Sharp Geometric Mean Bounds for Neuman Means |
| title_full | Sharp Geometric Mean Bounds for Neuman Means |
| title_fullStr | Sharp Geometric Mean Bounds for Neuman Means |
| title_full_unstemmed | Sharp Geometric Mean Bounds for Neuman Means |
| title_short | Sharp Geometric Mean Bounds for Neuman Means |
| title_sort | sharp geometric mean bounds for neuman means |
| url | http://dx.doi.org/10.1155/2014/949815 |
| work_keys_str_mv | AT yanzhang sharpgeometricmeanboundsforneumanmeans AT yumingchu sharpgeometricmeanboundsforneumanmeans AT yunliangjiang sharpgeometricmeanboundsforneumanmeans |