@article {
author = {Arab, R. and Allahyari, R. and Shole Haghighi, A.},
title = {Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {1},
pages = {53-67},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel\`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixed point theorem associated with these new measures of noncompactness. Further, some examples are presented to show the efficiency of our results.},
keywords = {Measure of noncompactness,Darbo's fixed point theorem,Arzela-Ascoli theorem,integral-differential equations},
url = {http://bims.iranjournals.ir/article_994.html},
eprint = {http://bims.iranjournals.ir/article_994_cd6cfba8a4671e144751135c1b54b0c3.pdf}
}