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Analogues of the parallelogram identity and the (CN) inequality of Bruhat and Tits in uniformly convex metric spaces are established. As an application of the new inequalities, we prove two fixed point results for single-valued and multi-valued Lipschitzian mappings. 相似文献
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Lagrange multiplier rules for extremals in linear spaces 总被引:1,自引:0,他引:1
Y. Nagahisa 《Journal of Optimization Theory and Applications》1981,33(2):223-240
The aim of this paper is to formulate extremals in real, linear spaces, and to derive necessary conditions in the form of Lagrange multiplier rules for the extremals. Using a separation of intrinsic cores in real, linear spaces, the multiplier rules are proved under some conditions.The author wishes to thank the referee for a number of valuable suggestions, particularly the proof of Theorem 3.1. 相似文献
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Summary In this paper we give a definition for the gradient of a functional defined on a normed linear space which in the case of Hilbert space reduces to the usual definition. We also establish some interesting properties of the gradient which allow us to extend the well-known theorem of Curry to a large class of normed linear spaces.A part of this research was sponsored by the U.S. Army under contract No. DA-31-124-ARO-D-462. 相似文献
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T. O. Banakh 《Functional Analysis and Its Applications》1994,28(4):285-286
L'vov State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 4, pp. 77–79, October–December, 1994. 相似文献
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《Topology and its Applications》1986,22(2):109-122
We write 2x for the hyperspace of all non-empty compact sets in a complete metric linear space X topologized by the Hausdorff metric. Using the notation (X) = {A ϵ 2X: A is finite}, lf2 = {x} = (xi) ϵ l2: xi = 0 for almost all i}, and lσ2 = {x = (x i) ϵ l2:σ∞i=1 (ixi)2 < ∞}, we have the following theorem:A family ⊂(X) is homeomorphic to lf2 if is σ-fd-compact, the closure of in 2x is not locally compact and if whenever A, B ∈ , λ ∈ [0, 1] and C ⊂ λA + (1 - λ)B with card C⩽ max{card A, card B} then C ϵ .Moreover, for any Gδ-AR-set of with ⊃ we have (, )≅(l2, lƒ2).Similar conditions for hyperspaces to be homeomorphic to lσ2 are also established. 相似文献
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Jensen's inequality is extended to metric spaces endowed with a convex combination operation. Applications include a dominated convergence theorem for both random elements and random sets, a monotone convergence theorem for random sets, and other results on set-valued expectations in metric spaces and on random probability measures. 相似文献
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SizweMabizela 《分析论及其应用》2003,19(2):121-129
Let (X,d) be a real metric linear space, with translation-invariant metric d and G a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X. We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation. 相似文献
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A. I. Vasil'ev 《Mathematical Notes》1972,11(6):396-401
An analog of the well known concept of bounded compactness from the theory of normed spaces is investigated in a linear metric space X. From the results obtained follows, for example, a sufficient condition for approximative compactness of a finite-dimensional subspace Lx.Translated from Matematicheskie Zametki, Vol. 11, No. 6, pp. 651–660, June, 1972. 相似文献
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Let(X,d,)be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions.Let ρ∈(1,∞),0p≤1≤q≤∞,p≠q,γ∈[1,∞)and ∈∈(0,∞).In this paper,the authors introduce the atomic Hardy space Hp,q,γ atb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ∈(μ)via the discrete coefficient K(ρ),p B,S,and prove that the Calder′on-Zygmund operator is bounded from Hp,q,γ,δmb,ρ(μ)(or Hp,q,γatb,ρ(μ))into Lp(μ),and from Hp,q,γ+1atb,ρ(ρ+1)(μ)into H p,q,γ,12(δ-νp+ν)mb,ρ(μ).The boundedness of the generalized fractional integral Tβ(β∈(0,1))from Hp1,q,γ,θmb,ρ(μ)(or Hp1,q,γatb,ρ(μ))into Lp2(μ)with 1/p2=1/p1-β is also established.The authors also introduce theρ-weakly doubling condition,withρ∈(1,∞),of the measure and construct a non-doubling measure satisfying this condition.If isρ-weakly doubling,the authors further introduce the Campanato space Eα,qρ,η,γ(μ)and show that Eα,qρ,η,γ(μ)is independent of the choices ofρ,η,γand q;the authors then introduce the atomic Hardy space Hp,q,γatb,ρ(μ)and the molecular Hardy space Hp,q,γ,mb,ρ(μ),which coincide with each other;the authors finally prove that Hp,q,γatb,ρ(μ)is the predual of E1/p-1,1ρ,ρ,1(μ).Moreover,if is doubling,the authors show that Eα,qρ,η,γ(μ)and the Lipschitz space Lipα,q(μ)(q∈[1,∞)),or Hp,q,γatb,ρ(μ)and the atomic Hardy space Hp,q at(μ)(q∈(1,∞])of Coifman and Weiss coincide.Finally,if(X,d,)is an RD-space(reverse doubling space)with(X)=∞,the authors prove that Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ)and Hp,q at(μ)coincide for any q∈(1,2].In particular,when(X,d,):=(RD,||,dx)with dx being the D-dimensional Lebesgue measure,the authors show that spaces Hp,q,γatb,ρ(μ),Hp,q,γ,mb,ρ(μ),Hp,q,γatb,ρ(μ)and Hp,q,γ,mb,ρ(μ)all coincide with Hp(RD)for any q∈(1,∞). 相似文献
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Our basic object in this paper is to establish calculus rules for coderivatives of multivalued mappings between Banach spaces. We consider the coderivative which is associated to some geometrical approximate subdifferential for functions.
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Song Wenhua 《分析论及其应用》2002,18(4):20-30
In this paper, we study the contraction linearity for metric projection in Lp spaces. A geometrical property of a subspace Y of Lp is given on which Pr is a contraction projection. 相似文献
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The paper contains a survey of papers reviewed in Ref. Zh. Matematika from 1953–1978 on the theory of linear operators in (mainly Hibert) spaces with indefinite metric and their applications to various domains of mathematics and mechanics. As a preliminary, the needed results on the geometry of spaces with indefinite metric are described.Translated from Itogi Nauki i Tekhniki, Matematicheskii Analiz, Vol. 17, pp. 113–206, 1979. 相似文献
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N. V. Nevesenko 《Mathematical Notes》1978,23(4):308-312
The relationships, are studied between strict suns [1] and sets with semicontinuous below metric projections, and also certain general properties of these classes of sets in linear normed spaces. There are characterized finite-dimensional normed spaces in which the class of strict suns coincides with the class of nonvacuous closed sets having semicontinuous below metric projections. It is proven that a P-connected [1] set with semicontinuous below (semicontinuous above) metric projections is V-connected [1].Translated from Matematicheskie Zametki, Vol. 23, No. 4, pp. 563–572, April, 1978. 相似文献
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Oleksiy Dovgoshey Dmytro Dordovskyi 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(2):100-113
The paper deals with pretangent spaces to general metric spaces. An ultrametricity criterion for pretangent spaces is found
and it is closely related to the metric betweenness in the pretangent spaces. 相似文献