Document Zbl 1060.26012

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A new necessary condition for existence of the Stieltjes integral. (English) Zbl 1060.26012

Real Anal. Exch. 30(2004-2005), No. 1, 207-216 (2005).

Summary: The paper is devoted to establishing a necessary condition for the existence of the Riemann-Stieltjes integral of continuous functions and simultaneously to finding a limit form of its relationship with the classical Riemann integral depending on a parameter. The technique for this study is based on changing the weighted first difference of a given function into the simple difference of a function determined by a first-order difference equation.

MSC:

26A42	Integrals of Riemann, Stieltjes and Lebesgue type
39A10	Additive difference equations

Keywords:

Riemann-Stieltjes integral; difference equation; weighted first difference

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