On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil

Umi Mahnuna Hanung; Milan Tvrdý

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 4, page 357-372
  • ISSN: 0862-7959

Abstract

top
In this paper we explain the relationship between Stieltjes type integrals of Young, Dushnik and Kurzweil for functions with values in Banach spaces. To this aim also several new convergence theorems will be stated and proved.

How to cite

top

Hanung, Umi Mahnuna, and Tvrdý, Milan. "On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil." Mathematica Bohemica 144.4 (2019): 357-372. <http://eudml.org/doc/294195>.

@article{Hanung2019,
abstract = {In this paper we explain the relationship between Stieltjes type integrals of Young, Dushnik and Kurzweil for functions with values in Banach spaces. To this aim also several new convergence theorems will be stated and proved.},
author = {Hanung, Umi Mahnuna, Tvrdý, Milan},
journal = {Mathematica Bohemica},
keywords = {Kurzweil integral; Young integral; Dushnik integral; Kurzweil-Stieltjes integral; Young-Stieltjes integral; Dushnik-Stieltjes integral; convergence theorem},
language = {eng},
number = {4},
pages = {357-372},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil},
url = {http://eudml.org/doc/294195},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Hanung, Umi Mahnuna
AU - Tvrdý, Milan
TI - On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 4
SP - 357
EP - 372
AB - In this paper we explain the relationship between Stieltjes type integrals of Young, Dushnik and Kurzweil for functions with values in Banach spaces. To this aim also several new convergence theorems will be stated and proved.
LA - eng
KW - Kurzweil integral; Young integral; Dushnik integral; Kurzweil-Stieltjes integral; Young-Stieltjes integral; Dushnik-Stieltjes integral; convergence theorem
UR - http://eudml.org/doc/294195
ER -

References

top
  1. Ashordia, M., 10.21136/mb.2016.15, Math. Bohem. 141 (2016), 183-215. (2016) Zbl06587862MR3499784DOI10.21136/mb.2016.15
  2. Dushnik, B., On the Stieltjes Integral, Thesis. University of Michigan, Ann Arbor (1931). (1931) MR2936614
  3. Federson, M., Bianconi, R., Barbanti, L., 10.1007/s10255-004-0200-0, Acta Math. Appl. Sin., Engl. Ser. 20 (2004), 623-640. (2004) Zbl1067.45005MR2173638DOI10.1007/s10255-004-0200-0
  4. Federson, M., Táboas, P., 10.1016/s0022-0396(03)00061-5, J. Differ. Equations 195 (2003), 313-331. (2003) Zbl1054.34102MR2016815DOI10.1016/s0022-0396(03)00061-5
  5. Hildebrandt, T. H., 10.1215/ijm/1255455257, Ill. J. Math. 3 (1959), 352-373. (1959) Zbl0088.31101MR0105600DOI10.1215/ijm/1255455257
  6. Hildebrandt, T. H., 10.1016/s0079-8169(08)x6120-3, Pure and Applied Mathematics 13. Academic Press, New York (1963). (1963) Zbl0112.28302MR0154957DOI10.1016/s0079-8169(08)x6120-3
  7. Hönig, C. S., Volterra Stieltjes-Integral Equations. Functional Analytic Methods; Linear Constraints, North-Holland Mathematics Studies 16. Notas de Mathematica (56). North-Holland Publishing Company, Amsterdam; American Elsevier Publishing Company, New York (1975). (1975) Zbl0307.45002MR0499969
  8. Hönig, C. S., 10.1007/bfb0089315, Functional Differential Equations and Bifurcation. Proc. Conf., Inst. Ciênc. Mat. São Carlos, 1979 Lecture Notes in Math. 799. Springer, Berlin (1980), 173-216 A. F. Izé. (1980) Zbl0436.45021MR0585488DOI10.1007/bfb0089315
  9. Kurzweil, J., 10.21136/CMJ.1957.100258, Czech. Math. J. 7 (1957), 418-449. (1957) Zbl0090.30002MR0111875DOI10.21136/CMJ.1957.100258
  10. Kurzweil, J., 10.1142/9789814324038, Series in Real Analysis 11. World Scientific, Hackensack (2012). (2012) Zbl1248.34001MR2906899DOI10.1142/9789814324038
  11. MacNerney, J. S., 10.1090/s0002-9904-1963-11039-3, Bull. Am. Math. Soc. 69 (1963), 803-805. (1963) Zbl0129.27004MR0153809DOI10.1090/s0002-9904-1963-11039-3
  12. Meng, G., Zhang, M., 10.1016/j.jde.2012.12.001, J. Differ. Equations 254 (2013), 2196-2232. (2013) Zbl1267.34014MR3007109DOI10.1016/j.jde.2012.12.001
  13. Monteiro, G. A., Slavík, A., Tvrdý, M., 10.1142/9432, Series in Real Analysis 15. World Scientific, Hackensack (2018). (2018) Zbl06758513MR3839599DOI10.1142/9432
  14. Monteiro, G. A., Tvrdý, M., 10.21136/MB.2012.142992, Math. Bohem. 137 (2012), 365-381. (2012) Zbl1274.26014MR3058269DOI10.21136/MB.2012.142992
  15. Monteiro, G. A., Tvrdý, M., 10.3934/dcds.2013.33.283, Discrete Contin. Dyn. Syst. 33 (2013), 283-303. (2013) Zbl1268.45009MR2972960DOI10.3934/dcds.2013.33.283
  16. Saks, S., Theory of the Integral, With two additional notes by Stefan Banach. Dover Publications, Mineola (1964). (1964) Zbl1196.28001MR0167578
  17. Schwabik, Š., On a modified sum integral of Stieltjes type, Čas. Pěst. Mat. 98 (1973), 274-277. (1973) Zbl0266.26007MR0322114
  18. Schwabik, Š., On the relation between Young's and Kurzweil's concept of Stieltjes integral, Čas. Pěst. Mat. 98 (1973), 237-251. (1973) Zbl0266.26006MR0322113
  19. Schwabik, Š., 10.1142/1875, Series in Real Analysis 5. World Scientific, Singapore (1992). (1992) Zbl0781.34003MR1200241DOI10.1142/1875
  20. Schwabik, Š., 10.21136/MB.1996.126036, Math. Bohem. 121 (1996), 425-447. (1996) Zbl0879.28021MR1428144DOI10.21136/MB.1996.126036
  21. Schwabik, Š., 10.21136/MB.1999.125994, Math. Bohem. 124 (1999), 433-457. (1999) Zbl0937.34047MR1722877DOI10.21136/MB.1999.125994
  22. Schwabik, Š., 10.21136/MB.2000.126273, Math. Bohem. 125 (2000), 431-454. (2000) Zbl0974.34057MR1802292DOI10.21136/MB.2000.126273
  23. Schwabik, Š., 10.21136/MB.2001.134198, Math. Bohem. 126 (2001), 613-629. (2001) Zbl0980.26005MR1970264DOI10.21136/MB.2001.134198
  24. Schwabik, Š., Tvrdý, M., Vejvoda, O., Differential and Integral Equations. Boundary Value Problems and Adjoints, D. Reidel Publishing Company, Dordrecht; Academia (Publishing House of the Czechoslovak Academy of Sciences), Praha (1979). (1979) Zbl0417.45001MR0542283
  25. Schwabik, Š., Ye, G., 10.1142/5905, Series in Real Analysis 10. World Scientific, Hackensack (2005). (2005) Zbl1088.28008MR2167754DOI10.1142/5905
  26. Young, W. H., 10.1112/plms/s2-13.1.109, Proc. Lond. Math. Soc. (2) 13 (1914), 109-150. (1914) Zbl45.0446.04MR1577495DOI10.1112/plms/s2-13.1.109

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.