Lebesgue-Stieltjes measure on time scales
Yıl: 2009 Cilt: 33 Sayı: 1 Sayfa Aralığı: 27 - 40 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022
Lebesgue-Stieltjes measure on time scales
Öz: The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes Δ and ∇-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes Δ-integral. We also establish the relation between Lebesgue- Stieltjes measure and Lebesgue-Stieltjes Δ-measure, consequently between Lebesgue-Stieltjes integral and Lebesgue-Stieltjes Δ- integral.
Anahtar Kelime: Konular:
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Bohner M., Peterson A., Eds.: “Advances in Dynamic Equations on Time Scales”, Birkhauser, Boston, 117–163 (2003).
- [2] Cabada, A. and Vivero, D.: “Expression of the Lebesgue Δ-Integral on Time Scales as a Usual Lebesgue Intregral; Application to the Calculus of Δ-Antiderivatives”, Mathematical and Computer Modelling, 43, 194-207 4, 291–310 (2006).
- [3] Carter M. and Brunt B. V.: “The Lebesgue-Stieltjes Integral”, (Springer-Verlag, NewYork) 2000.
- [4] Guseinov, G.S.: “Integration on Time Scales”, Journal of Mathematical Analysis & Applications, 285, 107–127 (2003).
- [5] Hilger, S.: “Ein Masskettenkalk¨ul mit Anwendung auf Zentrumsmanningfaltigkeiten”, (Ph.D. Thesis, Universitat Wrzburg) 1988.
- [6] Rzezuchowski, T.: “A Note on Measures on Time Scales”, Demonstratio Mathematica, 38, 1 79–84 (2005).
| APA | DENİZ A, UFUKTEPE Ü (2009). Lebesgue-Stieltjes measure on time scales. , 27 - 40. |
| Chicago | DENİZ Aslı,UFUKTEPE Ünal Lebesgue-Stieltjes measure on time scales. (2009): 27 - 40. |
| MLA | DENİZ Aslı,UFUKTEPE Ünal Lebesgue-Stieltjes measure on time scales. , 2009, ss.27 - 40. |
| AMA | DENİZ A,UFUKTEPE Ü Lebesgue-Stieltjes measure on time scales. . 2009; 27 - 40. |
| Vancouver | DENİZ A,UFUKTEPE Ü Lebesgue-Stieltjes measure on time scales. . 2009; 27 - 40. |
| IEEE | DENİZ A,UFUKTEPE Ü "Lebesgue-Stieltjes measure on time scales." , ss.27 - 40, 2009. |
| ISNAD | DENİZ, Aslı - UFUKTEPE, Ünal. "Lebesgue-Stieltjes measure on time scales". (2009), 27-40. |
| APA | DENİZ A, UFUKTEPE Ü (2009). Lebesgue-Stieltjes measure on time scales. Turkish Journal of Mathematics, 33(1), 27 - 40. |
| Chicago | DENİZ Aslı,UFUKTEPE Ünal Lebesgue-Stieltjes measure on time scales. Turkish Journal of Mathematics 33, no.1 (2009): 27 - 40. |
| MLA | DENİZ Aslı,UFUKTEPE Ünal Lebesgue-Stieltjes measure on time scales. Turkish Journal of Mathematics, vol.33, no.1, 2009, ss.27 - 40. |
| AMA | DENİZ A,UFUKTEPE Ü Lebesgue-Stieltjes measure on time scales. Turkish Journal of Mathematics. 2009; 33(1): 27 - 40. |
| Vancouver | DENİZ A,UFUKTEPE Ü Lebesgue-Stieltjes measure on time scales. Turkish Journal of Mathematics. 2009; 33(1): 27 - 40. |
| IEEE | DENİZ A,UFUKTEPE Ü "Lebesgue-Stieltjes measure on time scales." Turkish Journal of Mathematics, 33, ss.27 - 40, 2009. |
| ISNAD | DENİZ, Aslı - UFUKTEPE, Ünal. "Lebesgue-Stieltjes measure on time scales". Turkish Journal of Mathematics 33/1 (2009), 27-40. |
