![](/images/graphics-bg.png)
Integral Representation of Functions of Bounded Variation
Joint Authors
Lipcsey, Z.
Esuabana, I. M.
Ugboh, J. A.
Isaac, I. O.
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-07-08
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Functions of bounded variations form important transition between absolute continuous and singular functions.
With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations.
However, the determination of existence of solutions is still problematic because the solutions of differential equations is usually at least absolute continuous which is disrupted by the solutions of bounded variations.
As it is known, if f:[a,bλ]→Rn is of bounded variation then f is the sum of an absolute continuous function fa and a singular function fs where the total variation of fs generates a singular measure τ and fs is absolute continuous with respect to τ.
In this paper we prove that a function of bounded variation f has two representations: one is f which was described with an absolute continuous part with respect to the Lebesgue measure λ, while in the other an integral with respect to τ forms the absolute continuous part and t(τ) defines the singular measure.
Both representations are obtained as parameter transformation images of an absolute continuous function on total variation domain [a,bν].
American Psychological Association (APA)
Lipcsey, Z.& Esuabana, I. M.& Ugboh, J. A.& Isaac, I. O.. 2019. Integral Representation of Functions of Bounded Variation. Journal of Mathematics،Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1181351
Modern Language Association (MLA)
Lipcsey, Z.…[et al.]. Integral Representation of Functions of Bounded Variation. Journal of Mathematics No. 2019 (2019), pp.1-11.
https://search.emarefa.net/detail/BIM-1181351
American Medical Association (AMA)
Lipcsey, Z.& Esuabana, I. M.& Ugboh, J. A.& Isaac, I. O.. Integral Representation of Functions of Bounded Variation. Journal of Mathematics. 2019. Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1181351
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1181351