Das, A. G.; Kundu, Sarmila A generalized Henstock integral. (English) Zbl 1084.26004 Real Anal. Exch. 29(2003-2004), No. 1, 59-78 (2004). A specific integration based on the concept of \(\delta\)-fine tagged \(k\)-partitions is defined for functions \(U:[a,b]^{k=1} \to \mathbb R^n\) in the flavor of Henstock-Kurzweil integration. The resulting integral is called the \(GH_k\) integral. If \(k=1\) then the \(GH_1\) integral coincides with the integral described in the reviewers book “Generalized ordinary differential equations” (1992; Zbl 0781.34003). Basic results for the \(GH_k\) integral are presented (Saks-Henstock lemma, Cauchy extension) and in the introduction other similar concepts of integration are discussed. Reviewer: Štefan Schwabik (Praha) Cited in 1 ReviewCited in 1 Document MSC: 26A39 Denjoy and Perron integrals, other special integrals 26A42 Integrals of Riemann, Stieltjes and Lebesgue type Keywords:\(GH_k\) integral; Henstock-Kurzweil integral Citations:Zbl 0781.34003 × Cite Format Result Cite Review PDF Full Text: DOI