Author/Authors :
-، - نويسنده Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran. Arab, R. , -، - نويسنده Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Allahyari, R. , -، - نويسنده Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. Shole Haghighi, A.
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 Darboʹs fixed point theorem associated with these new measures of noncompactness. Further, some examples are presented to show the efficiency of our results.
