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1.
Approximation of set valued functions and fixed point theorems 总被引:6,自引:0,他引:6
Arrigo Cellina 《Annali di Matematica Pura ed Applicata》1969,82(1):17-24
Sommario Il risultato fondamentale della Nota è il seguente: siaΓ una multiapplicazione semicontinua superiormente da uno spazio metrico compatto S ad uno spazio normato Y, tale cheΓ(x) è convesso. Allora per ogniɛ>0 esiste una applicazione continua f: :S → Y tale che d*(F, G)<ɛ, ove F e G sono i grafici di f eΓ e d*(F, G)=sup {d(y, G), y ∈ F}.
Come corollari di questo teorema vengono dimostrati il teorema di punto fisso di Kakutani in uno spazio di Banach ed una sua
generalizzazione, che non richiede la compattezza diΓ(x). Viene poi presentato un teorema di punto fisso con condizioni di convessità più deboli di quello di Kakutani.
Entrata in Redazione il 14 gennaio 1969.
This work was performed while the author held the position of Faculty Research Assistant at the University of Maryland and was partially supported by the National Science Foundation under Grant GP-7846. 相似文献
Entrata in Redazione il 14 gennaio 1969.
This work was performed while the author held the position of Faculty Research Assistant at the University of Maryland and was partially supported by the National Science Foundation under Grant GP-7846. 相似文献
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We extend the Carathéodory-Julia theorem on angular derivatives as well as its higher order analogue established recently
in [4] to the setting of contractive valued functions analytic on the unit disk. Carathéodory-Julia type conditions for an
operator valued Schur-class function w are shown to be equivalent to the requirement that every function from the de Branges-Rovnyak space associated with w has certain directional boundary angular derivatives. 相似文献
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Necessary and sufficient conditions for a point to be a weak saddle point of a vector valued function (i.e. to be a solution of the vector saddle point problem) are given. Also, an existence result for a vector saddle point to have a solution is given. 相似文献
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《Journal de Mathématiques Pures et Appliquées》2006,85(3):313-344
We revisit studies on extension of Lipschitz maps and obtain new results about extension of displacements of bounded strain tensors. These questions are of interest in elasticity theory, optimal designs, as well as in functional analysis. 相似文献
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H.O. Fattorini 《Journal of Functional Analysis》1980,39(3):381-407
It was proved by Komatsu that both Roumieu and Beurling ultradistributions can be locally expressed in the form P(D)f, where f is a continuous function and P is a differential operator of infinite order. We prove here a more general result (valid for ultradistributions taking values in arbitrary normed spaces, not necessarily reflexive) based on an elementary probabilistic construction. Several extensions (to more general range spaces) are indicated. 相似文献
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Alessandro Trombetta 《Rendiconti del Circolo Matematico di Palermo》1932,56(1):65-78
In [11] Sion has investigated measures and integrals having values in uniform semigroups. In this paper a result which gives sufficient conditions for the existence of a unique product of semigroup valued measures is established. Moreover a convergence theorem for product integrals of semigroup valued functions is proved. 相似文献
10.
Alessandro Trombetta 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):65-78
In [11] Sion has investigated measures and integrals having values in uniform semigroups. In this paper a result which gives
sufficient conditions for the existence of a unique product of semigroup valued measures is established. Moreover a convergence
theorem for product integrals of semigroup valued functions is proved. 相似文献
11.
Characterization theorems for some classes of covariance functions associated to vector valued random fields 总被引:1,自引:0,他引:1
We characterize some important classes of cross-covariance functions associated to vector valued random fields based on latent dimensions. We also give some results for mixture based models that allow for the construction of new cross-covariance models. In particular, we give a criterion for the permissibility of quasi-arithmetic operators in order to construct valid cross covariances. 相似文献
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This paper contains three theorems on the order of approximation of 2π-periodic functions of two variables by some linear
means of the Fourier series in the Orlicz spaces. These theorems generalize some results given in [1] and [5]. 相似文献
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The derivative of a function defined on a set of matrices is given utilizing the Moore-Penrose pseudoinverse, which yields a natural extension of differentiation in the univariate calculus. Several mean value theorems involving this derivative are established. 相似文献
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Josef Janyška 《Central European Journal of Mathematics》2005,3(2):294-308
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent
bundle of a manifold with a linear (non-symmetric) connection.
This paper has been supported by the Grant Agency of the Czech Republic under the Project number GA 201/02/0225. 相似文献
16.
Yu. L. Ershov 《Siberian Mathematical Journal》2006,47(6):1027-1033
The literature on valued fields contains a series of the theorems referred to as root continuity theorems. The goal of this article is to improve the constants δ for three available theorems formulated in the language of ε and δ. The proofs rest on the basic proposition of the author’s article. 相似文献
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Michał Kisielewicz 《随机分析与应用》2018,36(3):495-520
The article is devoted to new properties of Aumann, Lebesgue, and Itô set-valued stochastic integrals considered in papers [1,2]. In particular, it contains some approximation theorems for Aumann and Itô set-valued stochastic integrals. Hence, in particular, it follows that Aumann and Lebesgue set-valued stochastic integrals cover a.s., both for measurable and IF-nonanticipative integrably bounded set-valued stochastic processes. 相似文献
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Let(Ω,Σ,μ)be a complete probability space and let X be a Banach space.We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem.We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on N. 相似文献
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M. Hasanov 《Journal of Mathematical Analysis and Applications》2008,342(2):766-772
Basis problems for self-adjoint matrix valued functions are studied. We suggest a new and nonstandard method to solve basis problems both in finite and infinite dimensional spaces. Although many results in this paper are given for operator functions in infinite dimensional Hilbert spaces, but to demonstrate practicability of this method and to present a full solution of basis problems, in this paper we often restrict ourselves to matrix valued functions which generate Rayleigh systems on the n-dimensional complex space Cn. The suggested method is an improvement of an approach given recently in our paper [M. Hasanov, A class of nonlinear equations in Hilbert space and its applications to completeness problems, J. Math. Anal. Appl. 328 (2007) 1487-1494], which is based on the extension of the resolvent of a self-adjoint operator function to isolated eigenvalues and the properties of quadratic forms of the extended resolvent. This approach is especially useful for nonanalytic and nonsmooth operator functions when a suitable factorization formula fails to exist. 相似文献