%0 Journal Article
%T Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Arab, R.
%A Allahyari, R.
%A Shole Haghighi, A.
%D 2017
%\ 02/22/2017
%V 43
%N 1
%P 53-67
%! Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations
%K Measure of noncompactness
%K Darbo's fixed point theorem
%K Arzela-Ascoli theorem
%K integral-differential equations
%R
%X 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.
%U http://bims.iranjournals.ir/article_994_cd6cfba8a4671e144751135c1b54b0c3.pdf