Integration by parts and other theorems for R\(^3\)S-integrals (Q1978965)

The paper is devoted to some basic properties of the integral introduced by the author in [Srivastava, H.~M.(ed.) et al., Analysis, geometry and groups: a~Riemann legacy volume, 2 vols. Palm Harbor, FL: Hadronic Press. Hadronic Press Collection of Original Articles. Part I, 289-312 (1993; Zbl 0918.26009)] and called by him the Refinement-Ross-Riemann-Stieltjes integral. This integral is equivalent to the \(\sigma \)-Young-Stieltjes integral [cf., e.g., \textit{T. H. Hildebrandt}, ``Introduction to the theory of integration'' (1963; Zbl 0112.28302)] and is covered by the modified Perron-Stieltjes (Kurzweil) integral [cf. \textit{Š. Schwabik}, Čas. Pěst. Mat. 98, 274-277 (1973; Zbl 0266.26007)]. In particular, he proves theorems on integration by parts and, moreover, in the context of Wiener's functions of bounded generalized variation, theorems analogous to the Helly-Bray theorem and some Riesz type representation theorems.