Year: 2024
Type: article
Abstract: We prove if $\alpha$ be a function of bounded variation on $[a,b]$, $[m_{i}, M_{i}] \subset \mathbb{R}$ be a closed interval for $1\leq i \leq n$, $f_{i}:[a,b]\to [m_{i}, M_{i}]$ be Riemann-Stieltjes integrable with respect to $\alpha$, and $G: \Pi_{i=1}^{i=n} [m_{i},M_{i}] \to \mathbb{R}$ be continuous, then $H=G\circ(f_{1}, \dots ,f_{n})$ is Riemann-Stieltjes integrable with respect to $\alpha$. Some other consequences, applications and counterexamples are also provided.
Author: Ali Parsian
Institution: Tafresh University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405682734