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1.
本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理. 相似文献
2.
Minimax inequalities of Ky Fan 总被引:2,自引:0,他引:2
In this paper, we found a new result by relaxing the condition of [1, Theorem 3]. As its direct consequence, we have obtained some new minimax inequalities of Ky Fan and minimax theorems. 相似文献
3.
Minimax Theorems for Set-Valued Mappings 总被引:1,自引:0,他引:1
In this paper, we deal with two types of minimax theorems for set-valued mappings and vector-valued functions. 相似文献
4.
本文研究集值映射向量优化问题的ε-超鞍点和ε-对偶定理。在集值映射是近似广义锥次似凸的假设下,利用ε-超有效解的标量化和Lagrange乘子定理,建立和证明了关于ε-超有效解的鞍点和对偶定理。 相似文献
5.
6.
本文建立了 Banach空间集值测度的 Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示. 相似文献
7.
Chen G. Y. Huang X. X. Hou S. H. 《Journal of Optimization Theory and Applications》2000,106(1):151-164
In this paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1–4. 相似文献
8.
袁春红 《数学的实践与认识》2014,(22)
首先在序拓扑线性空间中定义了集值映射多目标半定规划问题的KuhnTucker鞍点,在广义锥-次类凸条件下,讨论了此集值优化问题的弱有效解和Benson真有效性解与Kuhn-Tucker鞍点之间的关系. 相似文献
9.
在没有线性结构的一般集合上引入了函数的一种“凹(凸)”性概念,得到一个没有线性结构的FanKy不等式;在此基础上,在一般的拓扑空间上建立了极大极小定理,并把著名的鞍点定理推广到没有线性结构的拓扑空间上· 相似文献
10.
本文利用集值映射弱次梯度的Morea-Rockafellar定理,在内部(锥)-凸性假设下,得到了集值映射关于Henig有效性的Morea-Rockafellar定理.其结论为:在内部(锥)-凸条件下,两个集值映射和的Henig有效次梯度可以表示成它们Henig有效次梯度的和. 相似文献
11.
研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理. 相似文献
12.
在本文中,我们研究了一类集值严格集-压缩映象的一致极限映象.建立了这类一致极限映象的不动点指数理论,证明了某些正不动点定理.我们的定理推广了Fitzpatrick和Petryshyn的某些最近结果. 相似文献
13.
锥凸集值映射的基本性质 总被引:3,自引:0,他引:3
本文首先在R~m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立. 相似文献
14.
We first consider a complete metric space of nonexpansive set-valued mappings acting on a closed convex subset of a Banach space with a nonempty interior, and show that a generic mapping in this space has a fixed point. We then establish analogous results for two complete metric spaces of set-valued mappings with convex graphs. 相似文献
15.
We give conditions under which the distance from a point x to the set of fixed points of the composition of the set-valued mappings F and G is bounded by a constant times the smallest distance between F ?1(x) and G(x). This estimate allows us to significantly sharpen a result by T.-C. Lim [10] regarding fixed-points stability of set-valued contractions. A global version of the Lyusternik-Graves theorem is obtained from this estimate as well. We apply the generalization of Lim's result to establish one-sided Lipschitz properties of the solution mapping of a differential inclusion with a parameter. 相似文献
16.
A.P. Farajzadeh A. Amini-Harandi D. Baleanu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):708-712
In this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942-2949]. 相似文献
17.
Journal of Optimization Theory and Applications - 相似文献
18.
Chun-xue Wu Li-juan Zhang 《应用数学学报(英文版)》2007,23(3):489-494
For a Banach Space X Garcia-Falset introduced the coefficient R(X) and showed that if R(X) 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ||Tx - TY|| ≤ a||x - y|| + b||x - Ty|| for any x,y E X, where a,b ≥ 0, a + b ≤ 1. We show that if R(X) 〈 1/1+b then T has a fixed point in X. 相似文献
19.
集值Superpramart的上鞅逼近 总被引:6,自引:0,他引:6
李高明 《数学物理学报(A辑)》2000,20(2):163-168
文中讨论了可积随机集条件期望的若干性质,在此基础上给出了集值Superpramart的上鞅逼近,同时,证明了集值Superpramart 在Kuratowski-Mosco意义下的收敛定理。 相似文献
20.
In this article, we suggest and analyze two methods for finding fixed points of nonexpansive mappings in Banach spaces. We prove that the proposed methods converge strongly to a fixed point of nonexpansive mappings. 相似文献