Simple Properties and Existence Theorem for the Henstock-Kurzweil-Stieltjes Integral of Functions Taking Values on C[a,b] Space-valued Functions

Authors

  • Andrew Felix IV Suarez Cunanan Surigao Del Sur State University
  • Julius Benitez

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i1.3626

Keywords:

$\mathcal{C}[a, b]$ space-valued function, $\delta$-fine tagged division, Henstock--Kurzweil--Stieltjes integral, Continuity, Bounded variation.

Abstract

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.

Author Biography

  • Andrew Felix IV Suarez Cunanan, Surigao Del Sur State University
    Department of Natural Sciences and Mathematics

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Published

2020-01-31

Issue

Vol. 13 No. 1: (January 2020)

Section

Nonlinear Analysis

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How to Cite

Simple Properties and Existence Theorem for the Henstock-Kurzweil-Stieltjes Integral of Functions Taking Values on C[a,b] Space-valued Functions. (2020). European Journal of Pure and Applied Mathematics, 13(1), 130-143. https://doi.org/10.29020/nybg.ejpam.v13i1.3626