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

Document Type : Research Paper


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

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


‎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.


Main Subjects

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