On the measure of noncompactness in $L_p(\mathbb{R}^+)$ and applications to a product of $n$-integral equations

Authors

MOHAMED M. A. METWALI
VISHNU NARAYAN MISHRA

DOI

10.55730/1300-0098.3365

Abstract

In this article, we prove a new compactness criterion in the Lebesgue spaces $L_p({\mathbb{R}}^+), 1 \leq p < \infty$ and use such criteria to construct a measure of noncompactness in the mentioned spaces. The conjunction of that measure with the Hausdroff measure of noncompactness is proved on sets that are compact in finite measure. We apply such measure with a modified version of Darbo fixed point theorem in proving the existence of monotonic integrable solutions for a product of $n$-Hammerstein integral equations $n\geq 2$.

Keywords

Compactness criterion, measure of noncompactness, discontinuous solutions, Hammerstein integral equations, compact in finite measure

First Page

372

Last Page

386

Recommended Citation

METWALI, MOHAMED M. A. and MISHRA, VISHNU NARAYAN (2023) "On the measure of noncompactness in $L_p(\mathbb{R}^+)$ and applications to a product of $n$-integral equations," Turkish Journal of Mathematics: Vol. 47: No. 1, Article 24. https://doi.org/10.55730/1300-0098.3365
Available at: https://journals.tubitak.gov.tr/math/vol47/iss1/24