- Bounded convergence theorem for abstract Kurzweil-Stieltjes Integral, Monatshefte für Mathematik, July 2016, Volume 180, Issue 3, pp 409–434. [PDF – the first version]. This paper [the final version] is at present in Ch.1 and Ch.2 of the book, precisely the monograph, entitled “Kurzweil-Stieltjes Integral – Theory and Applications” by World Scientific Publishing. This book is recommended as a textbook for advanced university or PhD courses covering the theory of integration or differential equations. The applications of the Kurzweil-Stieltjes integral in functional analysis and generalized differential equations including the dynamical equations in this book are given. Click here-1 or here-2 about monographs in mathematics.
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Kurzweil integral; Young integral; Dushnik integral; Kurzweil-Stieltjes integral; Young-Stieltjes integral; Dushnik-Stieltjes integral; convergence theoremSummary:
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. - Harnack extension principle supporting the Kurzweil type Stieltjes integration, 2020. To appear. Since the values of the Kurzweil-Stieltjes integrals over [c,d], (c,d], [c,d), and (c,d) need not coincide for discontinuous integrator (see the paper 1 above), the Harnack extension principle cannot be extended straightforwardly as that one derived in the Henstock-Kurzweil integration.