共查询到20条相似文献,搜索用时 15 毫秒
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DIFFERENTIABILITYOFCONVEXFUNCTIONSANDASPLUNDSPACESChengLizin(程立新)ZhangFeng(张风)(Math.Section,Dept.ofPublicCourses,JianghanrPet... 相似文献
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A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS. 相似文献
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《数学物理学报(B辑英文版)》2005,25(3):395-400
A locally convex space is said to be a Gâteaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gâteaux differentiable in D. This paper shows that the product of a GDS and a family of separable Fréchet spaces is a GDS, and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS. 相似文献
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《Quaestiones Mathematicae》2013,36(4):299-313
ABSTRACT Let Λ be a scalar sequence space which is endowed with a normal locally convex topology. For a separated locally convex space E we denote by Λ(E) the vector space of all sequences g in E for which (>g(i),a<) ε Λ for all a ε E'. We define a locally convex topology ζ on Λ(E) and then characterize the dual of the ζ-closure (denoted by Λc (E)) of the finite sequences in Λ(E). We demonstrate the existence of a continuous projection from Λ(E)' onto a subspace of Λ(E)' which is isomorphic to Λc(E)'. Furthermore, we find a topological decomposition of Λα c (E)”, where one of the factors is isomorphic to Λ;α(E). These results are then applied to find necessary and sufficient conditions for Λα(E) to be semi-reflexive. A parallel development yields the same results for the space Λ(E') of all sequences f in E' for which (>x, f(i)<) ε Λ; for all x ε E, when E is barrelled. We conclude the paper by application of the results on vector sequence spaces to spaces of operators—including for instance, necessary and sufficient conditions for Lb (E,Λ;) and Lb (Λ,E) to be semi-reflexive. 相似文献
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一般化凸空间上的截口定理和变分不等式定理 总被引:3,自引:0,他引:3
摘要:本文利用Brouwer不动点定理或已知的KKM型定理,得到一般化凸空间上的截口定理.讨论了变分不等式解的存在性问题。对文中的相应结论进行了一般化和改进。 相似文献
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Banach空间上一类由算子导出的局部凸拓扑 总被引:1,自引:0,他引:1
本文我们研究了由半范簇{PT|T∈ψ(E,E1)}在E上导出的局部凸拓扑σE(E1),其中PT(x)=Tx的范数,x∈E。首先我们给出了拓扑σE(E1)=ω和σE(E1)=E上的范数的等价条件,接着讨论了在σE(E1)下的紧性与完备性,最后利用空间稠密特征和关于无穷基数幂等的Hessenberg定理进一步研究了σE(E1)与E上的范数的关系,证明了当E的稠密特征足够大时在ω和E上的范数间有无穷多个 相似文献
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Zhou Feng 《数学年刊B辑(英文版)》1998,19(3):249-254
§1.IntroductionLetEbearealBanachspace,notnecesarilyreflexive.LetΦ,Ψ:E→]-∞,∞]betwolowersemicontinuousconvexfunctions.Wedenote... 相似文献
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Yekini SHEHU 《数学物理学报(B辑英文版)》2014,(2):409-423
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gteaux differentiable norm. Assume that every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive mappings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, convex optimization problems, and split feasibility problems. Our result extends many recent important results. 相似文献
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凸函数的某些性质及其在凸损失下Bayes估计中的应用 总被引:1,自引:0,他引:1
邹原 《高校应用数学学报(A辑)》1992,7(4):594-602
本文从微分的角度给出了凸函数的充要条件及其某些性质.据此我们推广了1963年Degroot和Rao在凸损失下的Bayes估计的主要结果. 相似文献
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本文引进了一类集值映射的积分,研究了这种积分的若干性质.在此基础上,讨论了这种积分与抽象函数的Riemann积分、Bochner积分和Petits积分的关系. 相似文献
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代数多项式和指数型整函数在Besov空间中的逼近 总被引:4,自引:0,他引:4
用K-泛函定义了一类Besov空间,并分别用n阶代数多项式及指数为σ的整函数的最佳逼近阶给出了其特征的刻画。 相似文献
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61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has… 相似文献
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In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces. 相似文献
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OPTIMALITY CONDITIONS AND APPROXIMATE OPTIMALITY CONDITIONS IN LOCALLY LIPSCHITZ VECTOR OPTIMIZATION
《Optimization》2012,61(2):309-321
Abstract In this paper, we study constrained locally Lipschitz vector optimization problems in which the objective and constraint spaces are Hilbert spaces, the decision space is a Banach space, the dominating cone and the constraint cone may be with empty interior. Necessary optimality conditions for this type of optimization problems are derived. A sufficient condition for the existence of approximate efficient solutions to a general vector optimization problem is presented. Necessary conditions for approximate efficient solutions to a constrained locally Lipschitz optimization problem is obtained. 相似文献
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1.IntroductionInthispaperwewillgivesomesuitablesufficientconditionswhichassuretheclosednesspropertyofthedifferenceoftwoclosedconvexsetsingeneralBanachspaces,notnecessarilyrenekive.Theclosednessproblemweareconcernedwithisfrequentlyencounteredindifferentbranchesofappliedmathematics;forexample,thesolvabilityoflinearsystemsoverconeandthedualitytheoryofabstractmathematicalprogramming.OurmotivationcomesfromaBaiocchi-Gastaldi-TomarelliIsresult13]concernedwiththecaseofHilbertspace.FurlhermorelK5th.… 相似文献
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In this paper, the authors study the inclusion relations between Dirichlet type spaces DT and α-Bloch spacesβα by means of higher radial derivative. The strictness and the best possibility of the inclusion relations are shown with constructive methods.Furthermore, they sharpen one of the results when T = n, which proves that a conjecture in [7] is true. 相似文献
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Banach空间一阶微分方程终值问题的解 总被引:19,自引:2,他引:19
本文利用新的比较结果和半序理论研究Banach空间中一阶非线性微分方程终值问题的最小解和最大解的存在性,改进和推广了某些已知结果. 相似文献
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在实自反Banach空间中,引入并研究一类k-次增生型变分包含问题,证明了这类变分包含解的存在与唯一性,并在去掉α_n→0,β_n→0(n→∝)以及序列{x_n)和{_η(g(x_n))}有界限制的条件下,建立了k-次增生型变分包含和变分不等式解的具有混合误差的多步迭代序列的强收敛性定理,给出了收敛率的估计式,从而改进和推广了前人的研究结果. 相似文献