(untitled) (European Journal of Pure and Applied Mathematics, 2020)
Henstock–Kurzweil integral, a nonabsolute integral, is a natural extension of the Riemann integral that was studied independently by Ralph Henstock and Jaroslav Kurzweil. This paper will introduce the Henstock–Kurzweil–Stieltjes integral of C[a,b]-valued functions defined on a closed interval [f,g]C[a,b], where C[a,b] is the space of all continuous real-valued functions defined on [a,b]R. Some simple properties of this integral will be formulated including the Cauchy criterion and an existence theorem will be provided.