Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means
We present the best possible parameters α1,α2,β1,β2∈R and α3,β3∈(1/2,1) such that the double inequalities α1A(a,b)+(1-α1)C(a,b)<NQA(a,b)<β1A(a,b)+(1-β1)C(a,b),Aα2(a,b)C1-α2(a,b)<NQA(a,b)<Aβ2(a,b)C1-β2(a,b), and C[α3a+(1-α3)b,α3b+(1-α3)a]<NQA(a,b)<C[β3a+(1-β3)b,β3b+(1-β3)a] hold for...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5131907 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550724141056000 |
|---|---|
| author | Ying-Qing Song Wei-Mao Qian Yu-Ming Chu |
| author_facet | Ying-Qing Song Wei-Mao Qian Yu-Ming Chu |
| author_sort | Ying-Qing Song |
| collection | DOAJ |
| description | We present the best possible parameters α1,α2,β1,β2∈R and α3,β3∈(1/2,1) such that the double inequalities α1A(a,b)+(1-α1)C(a,b)<NQA(a,b)<β1A(a,b)+(1-β1)C(a,b),Aα2(a,b)C1-α2(a,b)<NQA(a,b)<Aβ2(a,b)C1-β2(a,b), and C[α3a+(1-α3)b,α3b+(1-α3)a]<NQA(a,b)<C[β3a+(1-β3)b,β3b+(1-β3)a] hold for all a,b>0 with a≠b and give several sharp inequalities involving the hyperbolic and inverse hyperbolic functions. Here, N(a,b), A(a,b), Q(a,b), and C(a,b) are, respectively, the Neuman, arithmetic, quadratic, and centroidal means of a and b, and NQA(a,b)=N[Q(a,b),A(a,b)]. |
| format | Article |
| id | doaj-art-c28a8270e2964b09820d8b04ff3d02b5 |
| 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-c28a8270e2964b09820d8b04ff3d02b52025-02-03T06:06:04ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/51319075131907Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal MeansYing-Qing Song0Wei-Mao Qian1Yu-Ming Chu2School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, ChinaSchool of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, ChinaSchool of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, ChinaWe present the best possible parameters α1,α2,β1,β2∈R and α3,β3∈(1/2,1) such that the double inequalities α1A(a,b)+(1-α1)C(a,b)<NQA(a,b)<β1A(a,b)+(1-β1)C(a,b),Aα2(a,b)C1-α2(a,b)<NQA(a,b)<Aβ2(a,b)C1-β2(a,b), and C[α3a+(1-α3)b,α3b+(1-α3)a]<NQA(a,b)<C[β3a+(1-β3)b,β3b+(1-β3)a] hold for all a,b>0 with a≠b and give several sharp inequalities involving the hyperbolic and inverse hyperbolic functions. Here, N(a,b), A(a,b), Q(a,b), and C(a,b) are, respectively, the Neuman, arithmetic, quadratic, and centroidal means of a and b, and NQA(a,b)=N[Q(a,b),A(a,b)].http://dx.doi.org/10.1155/2016/5131907 |
| spellingShingle | Ying-Qing Song Wei-Mao Qian Yu-Ming Chu Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means Journal of Function Spaces |
| title | Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means |
| title_full | Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means |
| title_fullStr | Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means |
| title_full_unstemmed | Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means |
| title_short | Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means |
| title_sort | optimal bounds for neuman mean using arithmetic and centroidal means |
| url | http://dx.doi.org/10.1155/2016/5131907 |
| work_keys_str_mv | AT yingqingsong optimalboundsforneumanmeanusingarithmeticandcentroidalmeans AT weimaoqian optimalboundsforneumanmeanusingarithmeticandcentroidalmeans AT yumingchu optimalboundsforneumanmeanusingarithmeticandcentroidalmeans |