期刊论文

Chu, Yu-Ming

英文

JOURNAL OF INEQUALITIES AND APPLICATIONS

1025-5834

2019

2019

1

1-13

10.1186/s13660-019-2124-5

The work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485) and the Natural Science Foundation of Huzhou City (Grant No. 2018YZ07).

本校为其他机构

In the article, we prove that λ1=1/2+[(2+log(1+2))/2]1/ν−1/2, μ1=1/2+6ν/(12ν), λ2=1/2+[(π+2)/4]1/ν−1/2 and μ2=1/2+3ν/(6ν) are the best possible parameters on the interval [1 / 2 , 1] such that the double inequalities Cν[λ1x+(1−λ1)y,λ1y+(1−λ1)x]A1−ν(x,y)<RQA(x,y)<Cν[μ1x+(1−μ1)y,μ1y+(1−μ1)x]A1−ν(x,y),Cν[λ2x+(1−λ2)y,λ2y+(1−λ2)x]A1−ν(x,y)<RAQ(x,y)<Cν[μ2x+(1−μ2)y,μ2y+(1−μ2)x]A1−ν(x,y) hold for all x, y> 0 with x≠ y and ν∈ [1 / 2 , ∞) , where A(x, y) is the arithmetic mean, C(x, y) i...