Construction of measures of noncompactness of Ck(Ω) and Ck0 and their application to functional integral-differential equations

‎In this paper‎, ‎first‎, ‎we investigate the construction of compact sets of Ck and Ck0‎ ‎by proving ``Ck‎,‎Ck0−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.