On Ky Fan's inequality
نویسندگان
چکیده
منابع مشابه
Some extensions on Fan Ky ’ s inequality
In this paper we study the inequalities of the determinants of the positive definite matrices and the invertible matrices by applying the integral method and matrix theory such that extensions of Fan Ky’s inequality are established. And then an improvement of Fan Ky’s inequality is given by using the positive definiteness of Gram matrix. Mathematics Subject Classification (2010): 15A15, 26D15.
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Let Pn,r (x) be the generalized weighted means. Let F(x) be a C1 function, y = y(x) an implicit decreasing function defined by f(x,y) = 0 and 0 < m < M ≤ m′, n ≥ 2, xi ∈ [m,M], yi ∈ [m′,M′]. Then for −1 ≤ r ≤ 1, if f ′ x/f ′ y ≤ 1, |(F(Pn,1(y))− F(Pn,r (y)))/(F(Pn,1(x)) − F(Pn,r (x)))| < (maxm′≤ξ≤M′ |F ′(ξ)|)/(minm≤η≤M |F ′(η)|) · M/m′. A similar result exists for f ′ x/f ′ y ≥ 1. By specifying...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2001
ISSN: 1331-4343
DOI: 10.7153/mia-04-21