共查询到18条相似文献,搜索用时 93 毫秒
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李志龙 《应用泛函分析学报》2010,12(2):132-136
讨论了φ凹(-φ凸)算子,得到了φ凹增(-φ凸减)算子不动点存在唯一性结果,并且给出了收敛到该不动点的迭代序列.该结果去掉了以往文献中的φ→0(t→0~+)这一条件,从而改进和推广了相关结果.作为应用,给出了一类的Sturm-Liouville边值问题的正解的存在唯一性结果. 相似文献
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凹凸算子和与积的不动点及固有元 总被引:1,自引:0,他引:1
本文获得线性半序空间正锥上α凹与-α凸算子的和与积存在不动点的充分条件,并给出了迭代程序与误差估计.还讨论了固有值与固有元之间的关系. 相似文献
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该文引入了φ凹-(-ψ)凸算子,统一处理了一类具有某种凹凸性的混合单调算子,在非紧非连续条件下,得到了算子的不动点的存在唯一性和迭代收敛性,进而得到了具有a凹-Guo凸,凹-Guo凸,μ0凹-凸,μ0凹-(-a)凸或α1凹-(-α2)凸等性质的混合单调算子的新不动点定理。 相似文献
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Ф凹(-φ)凸混合单调算子不动点存在惟一性及其应用 总被引:2,自引:0,他引:2
该文引入了Ф凹(-φ)凸算子,统一处理了一类具有某种凹凸性的混合单调算子,在非紧非连续的条件下,利用单调叠代技巧证明了不动点的存在惟一,进而得到了具有α凹-凸、凹-(-α)凸、α凹-Guo凸、凹-Guo凸、e凹-Guo凸、e凹-凸、e凹-(-α)凸以及α1凹-(-α)凸等性质的混合单调算子的新不动点定理,并将所获结果应用于Hammerstein非线性积分方程. 相似文献
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Two operators on the set ofn-person cooperative games are introduced, the minimarg operator and the maximarg operator. These operators can be seen as dual to each other. Some nice properties of these operators are given, and classes of games for which these operators yield convex (respectively, concave) games are considered. It is shown that, if these operators are applied iteratively on a game, in the limit one will yield a convex game and the other a concave game, and these two games will be dual to each other. Furthermore, it is proved that the convex games are precisely the fixed points of the minimarg operator and that the concave games are precisely the fixed points of the maximarg operator. 相似文献
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Zhan Dong LIANG Wen Xia WANG Sheng Jia LI 《数学学报(英文版)》2006,22(2):577-582
We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a weaker condition. 相似文献
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Bruce W. Lamar 《Journal of Global Optimization》1999,15(1):55-71
D.c. functions are functions that can be expressed as the sum of a concave function and a convex function (or as the difference of two convex functions). In this paper, we extend the class of univariate functions that can be represented as d.c. functions. This expanded class is very broad including a large number of nonlinear and/or nonsmooth univariate functions. In addition, the procedure specifies explicitly the functional and numerical forms of the concave and convex functions that comprise the d.c. representation of the univariate functions. The procedure is illustrated using two numerical examples. Extensions of the conversion procedure for discontinuous univariate functions is also discussed. 相似文献
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1.IntroductionAsthesimplestrepresentationofgeneralconservationlaws,thesingleconservationlawswithonespacevariablehavebeenthoroughlydiscussed.Inthecasesthatthefluxfunctionisconvexorconcave,P.D.LaxobtainedageneralexpressionofthesolutionsforCauchyproblems[2];inordertoguaranteetheuniquenessofthesolution,O.A.OlejnikpresentedherfamousE--conditionwhichcanbeappliedtogeneralconservationlawswithonespacevariablel4];TheLax'sconceptsofentropyfunctionsandrelatedinequalityalsocanbeusedinthisspecialcase[3]… 相似文献
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一类混合单调算子新的不动点定理及其应用 总被引:2,自引:0,他引:2
尹建东 《应用泛函分析学报》2009,11(3):268-273
引入了广义Φ凹(-φ)凸算子这一概念,在非紧非连续条件下,得到了混合单调算子的几个新的不动点存在唯一性定理.最后给出了一个应用. 相似文献
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Dah-Chin Luor 《Linear and Multilinear Algebra》2013,61(12):2504-2519
ABSTRACTNorm comparison inequalities for two integral operators with radial kernels are established. Sharp norm estimates for operators with monotone and convex/concave kernels are obtained. Integral analogues of Bennett's estimates for summability matrices are given. The exact operator norms with power weights are also obtained for a class of integral operators with radial quasimonotone kernels. 相似文献
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Meiyu Zhang 《Journal of Mathematical Analysis and Applications》2008,339(2):970-981
In this paper, ? convex −ψ concave mixed monotone operators are introduced and some new existence and uniqueness theorems of fixed points for mixed monotone operators with such convexity concavity are obtained. As an application, we give one example to illustrate our results. 相似文献
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In the paper, we explain what subsets of the lattice ℤ
n and what functions on the lattice ℤ
n could be called convex. The basis of our theory is the following three main postulates of classical convex analysis: concave
functions are closed under sums; they are also closed under convolutions; and the superdifferential of a concave function
is nonempty at each point of the domain. Interesting (and even dual) classes of discrete concave functions arise if we require
either the existence of superdifferentials and closeness under convolutions or the existence of superdifferentials and closeness
under sums. The corresponding classes of convex sets are obtained as the affinity domains of such discretely concave functions.
The classes of the first type are closed under (Minkowski) sums, and the classes of the second type are closed under intersections.
In both classes, the separation theorem holds true. Unimodular sets play an important role in the classification of such classes.
The so-called polymatroidal discretely concave functions, most interesting for applications, are related to the unimodular
system
. Such functions naturally appear in mathematical economics, in Gelfand-Tzetlin patterns, play an important role for solution
of the Horn problem, for describing submodule invariants over discrete valuation rings, and so on. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 86–93. 相似文献