Article
Keywords:
integration by parts; Kurzweil-Stieltjes integral; Perron-Stieltjes integral
Summary:
Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.
References:
[2] Hönig, Ch. S.:
Volterra Stieltjes-Integral Equations. North-Holland Publ. Comp., Amsterdam, 1975.
MR 0499969
[4] Kurzweil, J.:
Nichtabsolut konvergente Integrale. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980.
MR 0597703 |
Zbl 0441.28001
[6] Schwabik, Š.:
Generalized Ordinary Differential Equations. World Scientific, Singapore, 1992.
MR 1200241 |
Zbl 0781.34003
[7] Schwabik, Š., Tvrdý, M., Vejvoda O.:
Differential and Integral Equations. Academia & Reidel, Praha & Dordrecht, 1979.
MR 0542283
[8] Schwabik, Š.:
Linear Stieltjes integral equations in Banach spaces. Math. Bohem. 124 (1999), 433–457.
MR 1722877 |
Zbl 0937.34047
[9] Schwabik, Š.:
Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions. Math. Bohem. 125 (2000), 431–454.
MR 1802292 |
Zbl 0974.34057