期刊论文

Yang, Zhen-Hang

英文

JOURNAL OF MATHEMATICAL INEQUALITIES

1846-579X

2015

9

2

331-343

10.7153/jmi-09-27

Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11171307, 61374086]; Natural Science Foundation of Zhejiang ProvinceNatural Science Foundation of Zhejiang Province [LY13A010004]

本校为第一且通讯机构

Let p is an element of R, M be a bivariate mean, and M-p be defined by M-p(a, b) = M-1/p(a(p), b(p)) (p not equal 0) and M-0(a, b) = lim(p -> 0)M(p)(a, b). In this paper, we prove that the sharp inequalities L-2(a, b) < P(a, b) < NS1/2(a, b) < He(a, b) < A(2/3)(a, b) < I(a, b) < Z(1/3)(a, b) < Y-1/2(a, b) hold for all a, b > 0 with a not equal b, where L(a, b) = (a- b)/(loga - logb), P(a, b) = (a - b)/[2arcsin((a- b)/(a + b))], NS(a, b) =(a- b)/[2arcsinh ((a- b)/(a + b))], He(a, b) =(a + root ab+ b)/3, A(a, b) = (a + b)/2, I(a, b) = 1/e(a(a)/b(b))(1/)((a-b)), Z(a, b) = a(a/(a+b)) b(b/(a+b)) an...