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1.
Some random approximations and random fixed point theorems for 1-set-contractive random operators 总被引:3,自引:0,他引:3
Liu Li-Shan 《Proceedings of the American Mathematical Society》1997,125(2):515-521
In this paper, we will prove that the random version of Fan's Theorem (Math. Z. 112 (1969), 234-240) is true for 1-set-contractive random operator , where is a weakly compact separable closed ball in a Banach space and is a measurable space. This class of 1-set-contractive random operator includes condensing random operators, semicontractive random operators, LANE random operators, nonexpansive random operators and others. As applications of our theorems, some random fixed point theorems of non-self-maps are proved under various well-known boundary conditions.
2.
Tomá s Domí nguez Benavides Genaro Ló pez Acedo Hong-Kun Xu 《Proceedings of the American Mathematical Society》1996,124(3):831-838
Some random fixed point theorems for set-valued operators are obtained. The measurability of certain marginal maps is also studied. The underlying measurable space is not assumed to be a Suslin family.
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The aim of this paper is to prove some random fixed point theorems for asymptotically nonexpansive random operator defined
on an unbounded closed and starshaped subset of a Banach space.
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BinayakS.Choudhury 《分析论及其应用》2003,19(2):99-107
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case. 相似文献
7.
Xing-Hua ZhuJian-Zhong Xiao 《Applied mathematics and computation》2011,217(12):6004-6010
A new continuity theorem of minimum selection is presented for a continuous set-valued operator from a topological space into a Banach space with some uniform convexity. As applications, some problems concerning minimum right inverses for linear operators and minimum fixed points for condensing set-valued nonlinear operators are discussed. Also, the existence of minimum solutions for an integral inclusion is proved. 相似文献
8.
Naseer Shahzad 《Journal of Mathematical Analysis and Applications》2004,296(1):302-308
The paper presents new random fixed point results for pseudo-contractive random operators. 相似文献
9.
仿照距离空间,2-距离空间中的一些概念,引入了p-距离空间及p-距离空间中的一些基本概念.根据研究2-距离空间中不动点理论的思想和方法,利用泛函分析的理论,对p-距离空间中的不动点问题进行了研究.把2.距离空间中压缩型映像的不动点理论移植到了p-距离空间中,形成了p-距离空间中压缩型映像的一些基本不动点理论.其距.离空... 相似文献
10.
Objective: in this article, we discuss the approximate controllability problems of a new class of fractional impulsive stochastic partial integro-differential systems in separable Hilbert spaces. Methods: by applying the fractional calculus, the measure of noncompactness, properties of fractional resolvent operators and fixed point theorems. Results: we prove our main results without the hypotheses of compactness on the operator generated by the linear part of systems. Instead we suppose that the nonlinear term only satisfies a weakly compactness condition. Conclusion: the approximate controllability for the control systems with noncompact operators is established. Finally, an example is given for the illustration of the obtained theoretical results. 相似文献
11.
Let C be a nonempty subset of a topological vector space E. We state and prove new various fixed point theorems of Fan–Browder type for set-valued maps F:C→2E such that C⊂F(C) (called expansive), without assuming that the sets C and F(C) are convex or compact or equal, and E is Hausdorff. Let K be a convex subset of E and let C be a nonempty subset of K. Our proofs use a technique based on the investigations of the images of maps and restated for maps f:C×K→R∪{−∞,+∞} of G.X.-Z. Yuan’s results concerning the existence of equilibrium points and minimax inequalities for maps f:K×K→R∪{−∞,+∞}. Examples are provided. 相似文献
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Douglas Rizzolo 《Journal of Mathematical Analysis and Applications》2007,332(2):1063-1070
We define the infinite-dimensional simplex to be the closure of the convex hull of the standard basis vectors in R∞, and prove that this space has the fixed point property: any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces. 相似文献
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This paper is concerned with α-convex operators on ordered Banach spaces. A surjection theorem for 1-convex operators in order intervals is established by means of the properties of cone and monotone iterative technique. It is assumed that 1-convex operator A is increasing and satisfies Ay−Ax?M(y−x) for θ?x?y?v0, where θ denotes the zero element and v0 is a constant. Moreover, we prove a fixed point theorem for -convex operators by using fixed point theorem of cone expansion. In the end, we apply the fixed point theorem to certain integral equations. 相似文献
15.
D. B. Rokhlin 《Mathematical Notes》2007,81(3-4):543-548
For set-valued random sequences (G n) n=0 N with relatively open convex values G n(ω), we prove a new test for the existence of a sequence (x n) n=0 N of selectors adapted to the filtration and admitting an equivalent martingale measure. The statement is formulated in terms of the supports of regular upper conditional distributions of G n. This is a strengthening of the main result proved in our previous paper [1], where the openness of the set G n(ω) was assumed and a possible weakening of this condition was discussed. 相似文献
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Alexander Yu. Solynin 《Proceedings of the American Mathematical Society》2007,135(4):1181-1186
We answer a question raised by D. Mejía and Ch. Pommerenke by showing that the analytic fixed point function is hyperbolically convex in the unit disc.
17.
Tomonari Suzuki 《Journal of Mathematical Analysis and Applications》2008,340(1):752-755
We give an example which says that Mizoguchi-Takahashi's fixed point theorem for set-valued mappings is a real generalization of Nadler's. We also give a very simple proof of Mizoguchi-Takahashi's theorem. 相似文献
18.
Yong-Zhuo Chen 《Positivity》2008,12(4):643-652
Let A and H be two operators defined in an ordered Banach space such that
, and
, where . This paper discusses the conditions which will guarantee the existence of an asymptotically attractive fixed point for T = A + H.
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在Banach空间介绍一类意义更广的随机集值系统x(ω)∈F(ω,x(ω),y(ω)),y(ω)∈G(ω,x(ω),y(ω)),并且在一定条件下证明这类系统随机解的存在性,其中F和G是随机集值映射. 相似文献
20.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(6):1040-1059
In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained. 相似文献