دورية أكاديمية
Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
| العنوان: | Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean |
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| المؤلفون: | Wei-Mao Qian, Zai-Yin He, Hong-Wei Zhang, Yu-Ming Chu |
| المصدر: | Journal of Inequalities and Applications, Vol 2019, Iss 1, Pp 1-13 (2019) |
| بيانات النشر: | SpringerOpen, 2019. |
| سنة النشر: | 2019 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | Arithmetic mean, Quadratic mean, Contraharmonic mean, Schwab–Borchardt mean, Neuman mean, Two-parameter contraharmonic and arithmetic mean, Mathematics, QA1-939 |
| الوصف: | Abstract In the article, we prove that λ1=1/2+[(2+log(1+2))/2]1/ν−1/2 $\lambda _{1}=1/2+\sqrt{ [ (\sqrt{2}+ \log (1+\sqrt{2}) )/2 ]^{1/\nu }-1}/2$, μ1=1/2+6ν/(12ν) $\mu _{1}=1/2+\sqrt{6 \nu }/(12\nu )$, λ2=1/2+[(π+2)/4]1/ν−1/2 $\lambda _{2}=1/2+\sqrt{ [(\pi +2)/4 ] ^{1/\nu }-1}/2$ and μ2=1/2+3ν/(6ν) $\mu _{2}=1/2+\sqrt{3\nu }/(6\nu )$ are the best possible parameters on the interval [1/2,1] $[1/2, 1]$ such that the double inequalities Cν[λ1x+(1−λ1)y,λ1y+(1−λ1)x]A1−ν(x,y)0 $x, y>0$ with x≠y $x\neq y$ and ν∈[1/2,∞) $\nu \in [1/2, \infty )$, where A(x,y) $A(x, y)$ is the arithmetic mean, C(x,y) $C(x, y)$ is the contraharmonic mean, and RQA(x,y) $\mathcal{R}_{QA}(x, y)$ and RAQ(x,y) $\mathcal{R}_{AQ}(x, y)$ are two Neuman means. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 1029-242X |
| Relation: | http://link.springer.com/article/10.1186/s13660-019-2124-5; https://doaj.org/toc/1029-242X |
| DOI: | 10.1186/s13660-019-2124-5 |
| URL الوصول: | https://doaj.org/article/2ade35ee5ebb4fc1a6c48978cbc7fe10 |
| رقم الأكسشن: | edsdoj.2ade35ee5ebb4fc1a6c48978cbc7fe10 |
| قاعدة البيانات: | Directory of Open Access Journals |
Find this article in full text from Springer Verlag. 
Full Text Finder | تدمد: | 1029242X |
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| DOI: | 10.1186/s13660-019-2124-5 |