Results 11 to 20 of about 5,545 (117)
A generalization of Ky Fan's inequality [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 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 , ⋅M/m′ A similar result exists for . By specifying f(x, y) and F(x), we get various generalizations of Ky Fan′s inequality.
Peng Gao
doaj +6 more sources
Mathematical Inequalities & Applications, 2001 The authors prove the Ky-Fan like inequalities \({\mathfrak H_n( \underline a; \underline w)\over\mathfrak H_n' ( \underline a; \underline w)}\leq {\mathfrak G_n( \underline a; \underline w)\over\mathfrak G_n' ( \underline a; \underline w)}\), where the notation \(\mathfrak H_n' ( \underline a; \underline w)\) for \(\mathfrak H_n' ( 1-\underline a ...
Gavrea, Ioan, Trif, Tiberiu
semanticscholar +3 more sources
On Ky Fan's Inequality and Its Additive Analogue
Journal of Mathematical Analysis and Applications, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Alzer
semanticscholar +4 more sources
Some refinements of Ky Fan's inequality
Journal of Mathematical Analysis and Applications, 1992 Some refinements of Ky Fan's inequality have been given. Note that Theorem 4 was also proved by the reviewer [see Prilozi, Makedonska Akad. Nauk Umet., Odd. Mat.-Tekh. Nauki 11, 5-7 (1990)] as well as by the same author of this paper [see Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 34(82), 291-296 (1990; Zbl 0753.26010)].
S. Dragomir
semanticscholar +4 more sources
On an additive analogue of Ky Fan's inequality
Indagationes Mathematicae, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Alzer
semanticscholar +4 more sources
Refinements of Ky Fan's Inequality [PDF]
Proceedings of the American Mathematical Society, 1993 Let \(x_ k\in]0,1/2]\) \((k=1,\dots,n)\), \[ A_ n=(x_ 1+\cdots+x_ n)/n,\;A_ n'=(1-x_ 1+\cdots+1-x_ n)/n, \] \[ G_ n=(x_ 1x_ 2,\dots,x_ n)^{1/n},\;G_ n'=((1-x_ 1)(1-x_ 2)\dots(1-x_ n))^{1/n}. \] The author states that both (1) \((1-G_ n)/(1-A_ n)\) and (2) \((1-G_ n')/(1-A_ n')\) lie between \(A_ n'/G_ n'\) and \(A_ n/G_ n\) with equality iff \(x_ 1=x_ ...
H. Alzer
semanticscholar +3 more sources
, 2006 In this paper, Ky Fan's inequality on σ-compact set is applied to variational inclusions and n-person game theory. We give results of some variational inclusions and existence of non-cooperative equilibrium in n-person game on σ-compact set.
Funchun Yang, Congxin Wu, Qinghai He
semanticscholar +2 more sources
Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2018 It has been a long-standing problem posed by the first author in a conference in Marseille in 1990 to characterize semitopological semigroups which have common fixed point property when acting on a nonempty weak* compact convex subset of a dual Banach ...
Anthony To-Ming Lau, Yong Zhang
doaj +3 more sources
On a minimax inequality of Ky Fan [PDF]
Proceedings of the American Mathematical Society, 1987 An extension of a minimax inequality of Ky Fan is given. It is then used to generalize to the set-valued setting a fixed point theorem of Ky Fan.
Chung-Wei Ha
openaire +3 more sources
Generalized Equilibrium Problems Related to Ky Fan Inequalities [PDF]
Abstract and Applied Analysis, 2014 We study a generalized equilibrium problem by using a nonsymmetric extension of Ky Fan’s inequality. As an application, we present a fixed point type algorithm inspired by a model from Tada and Takahashi (2007).
Ionel Rovenţa
doaj +4 more sources