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253 results on '"26A39"'

251. On integrals of vector-valued functions on time scales

Author

Mieczysław Cichoń

Subjects
Riemann integral, 28B05, 26A39, 39A12, 39A10, time scale, Pettis integral, 26A42, Henstock-Kurzweil integral, 28A25, dynamic Cauchy problem
Abstract

The main goal of the paper is to define new type of integrals for vector-valued functions on time scales. This allows to make possible the advantages of dynamic equations also for vector-valued functions i.e. for dynamic modeling in Banach spaces. To do it we define some appropriate integrals for vector-valued functions on time scales and we prove their properties. We emphasize on the particular ones, which are useful for solving dynamic equations in Banach spaces.

252. Convergence theorems for the Henstock integral involving small Riemann sums

Author

Soeparna Darmawijaya, Ch. Rini Indrati, Subanar, and Bambang Soedijono

Subjects
Discrete mathematics, Uniformly Strong Lusin Condition, Pure mathematics, Uniformly Functionally Small Riemann sum, $\delta$-fine partition, Partition of an interval, Mathematics::Classical Analysis and ODEs, Henstock Integral, Riemann Xi function, symbols.namesake, 26A39, Equi-Henstock integrability, Riemann sum, Convergence (routing), symbols, Functionally Small Riemann Sum, Geometry and Topology, Analysis, Mathematics
Abstract

We generalize the functionally-small-Riemann-sum (FSRS) property for the Henstock integral to the $n$-dimensional Euclidean space. We prove a convergence theorem and its connection with the equi-integrability condition.

253. The riemann-stieltjes integral on time scales

Author

Mozyrska, D., Ewa Pawluszewicz, and Torres, D. F. M.

Subjects
93C70, 26A39, Mathematics - Classical Analysis and ODEs, 39A12, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 26A42, Riemann-Stieltjes integral, Time scales, Delta and nabla integrals
Abstract

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given., Accepted (March 6, 2009) for publication at The Australian Journal of Mathematical Analysis and Applications (AJMAA), http://ajmaa.org

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