排序方式: 共有13条查询结果,搜索用时 15 毫秒
1.
2.
3.
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions. 相似文献
4.
It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential
equations (GODEs). In this paper, some stability concepts for retarded functional differential equations are introduced and
they are discussed using known stability results for GODEs. Then the equivalence of the different concepts of stabilities
considered here are proved and converse Lyapunov theorems for a very wide class of retarded functional differential equations
are obtained by means of the correspondence of this class of equations with GODEs.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 107–126, January, 2008. 相似文献
5.
6.
7.
Štefan Schwabik 《Mathematica Slovaca》2009,59(6):731-752
For a given continuous function F on a compact interval E in the set ? of reals the problem is how to describe the “total change” of F on a set M ? E. Full variational measures W F (M) and V F (M) (see Section 2) in the sense presented by B. S. Thomson are introduced in this work to this aim. They are generated by two slightly different interval functions, namely the oscillation of F over an interval and the value of the additive interval function generated by F, respectively. They coincide with the concept of classical total variation if M is an interval and they are zero if on the set M the function F is of negligible variation. The Kurzweil-Henstock integration is shortly described and some of its properties are studied using the variational measure W F (M) for the indefinite integral F of an integrable function f. 相似文献
8.
The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties
of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration).
It is shown that the indefinite McShane product integral of a matrix-valued function A is absolutely continuous. As a consequence we obtain that the McShane product integral of A over [a, b] exists and is invertible if and only if A is Bochner integrable on [a, b].
Supported by grant No. 201/04/0690 of the Grant Agency of the Czech Republic. 相似文献
9.
10.
This article studies some convergence results for the McShane integral of func- tions mapping the interval[0,1]into a Banach space X from the point of view of an open problem propose by D.H.Fremlin and J.Mendoza in[2].also the anthors give a negative answer to this open problem. 相似文献