Arab, R., Allahyari, R., Shole Haghighi, A. (2017). Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations. Bulletin of the Iranian Mathematical Society, 43(1), 53-67.

R. Arab; R. Allahyari; A. Shole Haghighi. "Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations". Bulletin of the Iranian Mathematical Society, 43, 1, 2017, 53-67.

Arab, R., Allahyari, R., Shole Haghighi, A. (2017). 'Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations', Bulletin of the Iranian Mathematical Society, 43(1), pp. 53-67.

Arab, R., Allahyari, R., Shole Haghighi, A. Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations. Bulletin of the Iranian Mathematical Society, 2017; 43(1): 53-67.

Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations

^{1}Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.

^{2}Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

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.

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