Open AccessSimple Properties and Existence Theorem for the Henstock-Kurzweil-Stieltjes Integral of Functions Taking Values on C[a,b] Space-valued Functions
Author(s) -
Andrew Felix IV Suarez Cunanan,
Julius V. Benitez
Publication year - 2020
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v1i1.3626
Subject(s) - mathematics , riemann–stieltjes integral , simple (philosophy) , riemann integral , daniell integral , space (punctuation) , extension (predicate logic) , cauchy's integral formula , pure mathematics , improper integral , cauchy distribution , mathematical analysis , integral equation , singular integral , cauchy problem , initial value problem , philosophy , linguistics , epistemology , computer science , programming language
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 $\mathcal{C}[a,b]$-valued functions defined on a closed interval $[f,g]\subseteq\mathcal{C}[a,b]$, where $\mathcal{C}[a,b]$ is the space of all continuous real-valued functions defined on $[a,b]\subseteq\mathbb{R}$. Some simple properties of this integral will be formulated including the Cauchy criterion and an existence theorem will be provided.