Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43120170222Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations5367994ENR. ArabDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.R. AllahyariDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.A. Shole HaghighiDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.Journal Article20141217In 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.http://bims.iranjournals.ir/article_994_cd6cfba8a4671e144751135c1b54b0c3.pdf