Remarks on incorrect measure of noncompactness in $\mathrm{BC}({\mathbb{R}}_{+}\times {\mathbb{R}}_{+})$

Abstract

In this paper, we indicate an error occurring in a few articles. This error concerns a certain measure of noncompactness in the space $\mathrm{BC}({\mathbb{R}}_{+}\times {\mathbb{R}}_{+})$. We show how this error could be corrected. Moreover, we propose a more convenient approach using the more general Fréchet space $C({\mathbb{R}}_{+}\times {\mathbb{R}}_{+})$ in which we indicate a simpler measure of noncompactness.