Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean
The authors find the greatest value λ and the least value μ, such that the double inequality C¯(λa+(1-λb),λb+(1-λ)a)<αA(a,b)+(1-α)T(a,b)<C¯(μa+(1-μ)b,μb+(1-μ)a) holds for all α∈(0,1) and a,b>0 with a≠b, where C¯(a,b)=2(a2+ab+b2)/3(a+b), A(a,b)=(a+b)/2, and Ta,b=2/π∫0π/2a2cos2θ+b2sin2θdθ den...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/842542 |
| id |
doaj-8c03230060db4b27bbf06298be93dec4 |
|---|---|
| record_format |
Article |
| spelling |
doaj-8c03230060db4b27bbf06298be93dec42020-11-25T02:30:48ZengHindawi LimitedThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/842542842542Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal MeanWei-Dong Jiang0Department of Information Engineering, Weihai Vocational College, Weihai, Shandong 264210, ChinaThe authors find the greatest value λ and the least value μ, such that the double inequality C¯(λa+(1-λb),λb+(1-λ)a)<αA(a,b)+(1-α)T(a,b)<C¯(μa+(1-μ)b,μb+(1-μ)a) holds for all α∈(0,1) and a,b>0 with a≠b, where C¯(a,b)=2(a2+ab+b2)/3(a+b), A(a,b)=(a+b)/2, and Ta,b=2/π∫0π/2a2cos2θ+b2sin2θdθ denote, respectively, the centroidal, arithmetic, and Toader means of the two positive numbers a and b.http://dx.doi.org/10.1155/2013/842542 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wei-Dong Jiang |
| spellingShingle |
Wei-Dong Jiang Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean The Scientific World Journal |
| author_facet |
Wei-Dong Jiang |
| author_sort |
Wei-Dong Jiang |
| title |
Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean |
| title_short |
Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean |
| title_full |
Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean |
| title_fullStr |
Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean |
| title_full_unstemmed |
Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean |
| title_sort |
bounds for combinations of toader mean and arithmetic mean in terms of centroidal mean |
| publisher |
Hindawi Limited |
| series |
The Scientific World Journal |
| issn |
1537-744X |
| publishDate |
2013-01-01 |
| description |
The authors find the greatest value λ and the least value μ, such that the double inequality C¯(λa+(1-λb),λb+(1-λ)a)<αA(a,b)+(1-α)T(a,b)<C¯(μa+(1-μ)b,μb+(1-μ)a) holds for all α∈(0,1) and a,b>0 with a≠b, where C¯(a,b)=2(a2+ab+b2)/3(a+b), A(a,b)=(a+b)/2, and Ta,b=2/π∫0π/2a2cos2θ+b2sin2θdθ denote, respectively, the centroidal, arithmetic, and Toader means of the two positive numbers a and b. |
| url |
http://dx.doi.org/10.1155/2013/842542 |
| work_keys_str_mv |
AT weidongjiang boundsforcombinationsoftoadermeanandarithmeticmeanintermsofcentroidalmean |
| _version_ |
1724827806916935680 |