Generalized Schwabik-Henstock integral (Q2771178)

The paper deals with the definition of a generalized integral, called Schwabik-Henstock integral, that extends several concepts of known integrals: Riemann integral, Riemann-Stieltjes integral, generalized Perron integral [\textit{Š. Schwabik}, ``Generalized ordinary differential equations'' (1992; Zbl 0781.34003)], and \(HS_k\) integral [\textit{A. G. Das, M. C. Nath} and \textit{G. Sahu}, Bull. Inst. Math. Acad. Sin. 26, No. 1, 61-75 (1998; Zbl 0933.26002)]. NEWLINENEWLINENEWLINEThis integral is introduced by means of a pair of functions \((U,V)\), where \(U\) and \(V\) are real functions defined on the square \([a,b] \times [a,b]\). The obtained integral possesses standard properties that include Saks-Henstock lemma, monotone and dominated convergence theorems, etc.