New extension of the variational McShane integral of vector-valued functions

Sokol Bush Kaliaj

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 2, page 137-148
  • ISSN: 0862-7959

Abstract

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We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset G of m -dimensional Euclidean space ℝ m . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from m -dimensional closed non-degenerate intervals to open and bounded subsets of ℝ m . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our integral to the study of the variational McShane integral. As an application, a full descriptive characterization of the Hake-variational McShane integral is presented in terms of the cubic derivative.

How to cite

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Kaliaj, Sokol Bush. "New extension of the variational McShane integral of vector-valued functions." Mathematica Bohemica 144.2 (2019): 137-148. <http://eudml.org/doc/294457>.

@article{Kaliaj2019,
abstract = {We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset $G$ of $m$-dimensional Euclidean space $\mathbb \{R\}^\{m\}$. It is a “natural” extension of the variational McShane integral (the strong McShane integral) from $m$-dimensional closed non-degenerate intervals to open and bounded subsets of $\mathbb \{R\}^\{m\}$. We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our integral to the study of the variational McShane integral. As an application, a full descriptive characterization of the Hake-variational McShane integral is presented in terms of the cubic derivative.},
author = {Kaliaj, Sokol Bush},
journal = {Mathematica Bohemica},
keywords = {Hake-variational McShane integral; variational McShane integral; Banach space; $m$-dimensional Euclidean space},
language = {eng},
number = {2},
pages = {137-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New extension of the variational McShane integral of vector-valued functions},
url = {http://eudml.org/doc/294457},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Kaliaj, Sokol Bush
TI - New extension of the variational McShane integral of vector-valued functions
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 2
SP - 137
EP - 148
AB - We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset $G$ of $m$-dimensional Euclidean space $\mathbb {R}^{m}$. It is a “natural” extension of the variational McShane integral (the strong McShane integral) from $m$-dimensional closed non-degenerate intervals to open and bounded subsets of $\mathbb {R}^{m}$. We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our integral to the study of the variational McShane integral. As an application, a full descriptive characterization of the Hake-variational McShane integral is presented in terms of the cubic derivative.
LA - eng
KW - Hake-variational McShane integral; variational McShane integral; Banach space; $m$-dimensional Euclidean space
UR - http://eudml.org/doc/294457
ER -

References

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