On Some Generalizations and Refinements of a Ky Fan Inequality
Copyright policy )On Some Generalizations and Refinements of a Ky Fan Inequality
This paper proves various extensions of the Ky Fan inequality and also gives an interesting proof, using Levinson 's inequality, of a previous extension by the same author [Southeast Asian Bull. Math. 22, No. 4, 363-372 (1998; Zbl 0947.26022)]. In particular we have the following results: for any \(k\geq 1\), \[ (k-G_n')/(k-A_n')\leq A_n/G_n \] and if \(2G_n'\geq k\geq A_n'\) then \[ A_n'/G_n'\leq (k-G_n')/(k-A_n'); \] when \(k=1\) these inequalities reduce to results of \textit{H. Alzer} [Acta Appl. Math. 38, No. 3, 305-354 (1995; Zbl 0834.26013)], and Jiang; here \(A_n, G _n\) are the weighted arithmetic and geometric means of \(x_i, 0
- Hong Kong Polytechnic University China (People's Republic of)
geometric mean, Inequalities for sums, series and integrals, Ky Fan's inequality, Means, arithmetic mean
geometric mean, Inequalities for sums, series and integrals, Ky Fan's inequality, Means, arithmetic mean
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!