共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper deals with the relation between the McShane integral and the Henstock–Kurzweil integral for the functions mapping a compact interval into a Banach space X and some other questions in connection with the McShane integral and the Henstock–Kurzweil integral of Banach space-valued functions. We prove that if a Banach space-valued function f is Henstock–Kurzweil integrable on I0 and satisfies Property (P), then I0 can be written as a countable union of closed sets En such that f is McShane integrable on each En when X contains no copy of c0. We further give an answer to the Karták's question. 相似文献
2.
Robert C. Stolz 《Proceedings of the American Mathematical Society》1997,125(4):1215-1220
For each function that satisfies the law of large numbers with values in a certain class of locally convex spaces with the Radon-Nikodym property the following decomposition holds: , where is integrable by seminorm, and is a Pettis integrable function which is scalarly 0.
3.
Jun Kawabe 《Proceedings of the American Mathematical Society》1996,124(5):1513-1515
The purpose of this paper is to show that a theorem of A. Wisniewski remains valid without the approximation property.
4.
Let X be a Banach space with a Schauder basis { en }, and let Φ( I ) = Σ∞ n=1 en∫I fn(t)dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Henstock-Kurzweil. Necessary and sufficient conditions are given for Φ to be the indefinite integral of a Henstock-Kurzweil-Pettis (or Henstock, or variational Henstock) integrable function f : [0, 1] → X . 相似文献
5.
V. Marraffa 《Journal of Mathematical Analysis and Applications》2004,293(1):71-78
Absolutely summing operators between Banach spaces are characterized by means of McShane integrable functions. 相似文献
6.
Hüseyin Budak Samet Erden Muhammad Aamir Ali 《Mathematical Methods in the Applied Sciences》2021,44(1):378-390
We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study. 相似文献
7.
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
8.
This paper deals with the study of a mathematical model of photon transport in an interstellar cloud where a localized source is present. The source is represented by a Dirac delta functional. The problem is studied in the setting of locally convex spaces. By means of the theory of semigroups on locally convex spaces and the adjoint approach, we prove existence and uniqueness of the solution. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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10.
Walter Roth 《Proceedings of the American Mathematical Society》1998,126(7):1973-1982
We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.
11.
José Rodríguez 《Journal of Mathematical Analysis and Applications》2006,316(2):579-600
Let (Ω,Σ,μ) be a complete probability space and an absolutely summing operator between Banach spaces. We prove that for each Dunford integrable (i.e., scalarly integrable) function the composition u○f is scalarly equivalent to a Bochner integrable function. Such a composition is shown to be Bochner integrable in several cases, for instance, when f is properly measurable, Birkhoff integrable or McShane integrable, as well as when X is a subspace of an Asplund generated space or a subspace of a weakly Lindelöf space of the form C(K). We also study the continuity of the composition operator f?u○f. Some other applications are given. 相似文献
12.
讨论了局部凸空间中推广的Leray-Schauder度的基本性质,建立了一些新的不动点定理,并给出了对局部凸空间Cauchy初值问题的应用.这些定理是Banach空间中相应结果的推广. 相似文献
13.
José Bonet José A. Conejero 《Proceedings of the American Mathematical Society》2001,129(12):3683-3690
If the set of monomorphisms between locally convex spaces is not empty, then it is an open subset of the space of all continuous and linear operators endowed with the topology of the uniform convergence on the bounded sets if and only if the domain space is normable. The corresponding characterization for the set of almost open operators is also obtained; it is related to the lifting of bounded sets and to the quasinormability of the domain space. Other properties and examples are analyzed.
14.
J. Ka?kol 《Journal of Mathematical Analysis and Applications》2007,332(2):965-974
Very recently Tkachuk has proved that for a completely regular Hausdorff space X the space Cp(X) of continuous real-valued functions on X with the pointwise topology is metrizable, complete and separable iff Cp(X) is Baire (i.e. of the second Baire category) and is covered by a family of compact sets such that Kα⊂Kβ if α?β. Our general result, which extends some results of De Wilde, Sunyach and Valdivia, states that a locally convex space E is separable metrizable and complete iff E is Baire and is covered by an ordered family of relatively countably compact sets. Consequently every Baire locally convex space which is quasi-Suslin is separable metrizable and complete. 相似文献
15.
Deformation in locally convex topological linear spaces 总被引:1,自引:0,他引:1
DING YanhengInstitute of Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2004,47(5):687-710
We are concerned with a deformation theory in locally convex topological linear spaces. A special "nice" partition of unity is given. This enables us to construct certain vector fields which are locally Lipschitz continuous with respect to the locally convex topology. The existence, uniqueness and continuous dependence of flows associated to the vector fields are established. Deformations related to strongly indefinite functionals are then obtained. Finally, as applications, we prove some abstract critical point theorems. 相似文献
16.
A. P. Solodov 《Mathematical Notes》1999,65(6):723-730
We solve the problem of the equivalence of theH L-integral and the Henstock integral in Banach spaces. Namely, we prove that the Saks-Henstock lemma is valid in a Banach space if and only if it is finite-dimensional. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 860–870, June, 1999. 相似文献
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18.
Rabha W.Ibrahim 《高校应用数学学报(英文版)》2009,24(2):175-183
The existence of continuous solutions for fractional integral inclusion via its singlevalued problem and fixed point theorem for set-valued function in locally convex topological spaces is discussed. The proof of the single-valued problem will be based on the Leray- Schauder fixed point theorem. Moreover, the controllability of this solution is studied. 相似文献
19.
New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values 总被引:1,自引:1,他引:0
N. A. Sokolov 《Computational Mathematics and Mathematical Physics》2007,47(12):1952-1969
New variants of the generalized level method for minimization of convex Lipschitz functions on a compact set with a nonempty interior are proposed. These variants include the well-known generalized and classical level methods. For the new variants, an estimate of the convergence rate is found, including the variants in which the auxiliary problems are solved approximately. 相似文献
20.
Ján Haluška 《Czechoslovak Mathematical Journal》1997,47(2):205-219
A generalization of I. Dobrakov's integral to complete bornological locally convex spaces is given. 相似文献