A note on integration by parts for abstract Perron-Stieltjes integrals
Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 613-629

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MR Zbl
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.
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.
DOI : 10.21136/MB.2001.134198
Classification : 26A39
Keywords: integration by parts; Kurzweil-Stieltjes integral; Perron-Stieltjes integral
Schwabik, Štefan. A note on integration by parts for abstract Perron-Stieltjes integrals. Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 613-629. doi: 10.21136/MB.2001.134198
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[1] Henstock, R.: Integration by parts. Aequationes Mathematicae 9 (1973), 1–18. | DOI | MR | Zbl

[2] Hönig, Ch. S.: Volterra Stieltjes-Integral Equations. North-Holland Publ. Comp., Amsterdam, 1975. | MR

[3] Kurzweil, J.: On integration by parts. Czechoslovak Math. J. 8 (1958), 356–359. | MR | Zbl

[4] Kurzweil, J.: Nichtabsolut konvergente Integrale. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. | MR | Zbl

[5] Schwabik, Š.: Abstract Perron-Stieltjes integral. Math. Bohem. 121 (1996), 425–447. | MR | Zbl

[6] Schwabik, Š.: Generalized Ordinary Differential Equations. World Scientific, Singapore, 1992. | MR | Zbl

[7] Schwabik, Š., Tvrdý, M., Vejvoda O.: Differential and Integral Equations. Academia & Reidel, Praha & Dordrecht, 1979. | MR

[8] Schwabik, Š.: Linear Stieltjes integral equations in Banach spaces. Math. Bohem. 124 (1999), 433–457. | MR | Zbl

[9] Schwabik, Š.: Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions. Math. Bohem. 125 (2000), 431–454. | MR | Zbl

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