标题：Construction of measures of noncompactness of DC n [ J , E ] $\mathit{DC}^{n}[J,E]$ and C 0 n [ J , E ] $C^{n}_{0}[J,E]$ with application to the solvability of n th-order integro-differential equations in Banach spaces
摘要：In the present paper, we first investigate the construction of compact sets of DC n [ J , E ] $\mathit{DC}^{n}[J,E]$ and C 0 n [ J , E ] $C^{n}_([J,E]$ , and then we introduce new measures of noncompactness on these spaces. In addition, as an application, we discuss the existence of solutions of initial value problems for nth-order nonlinear integro-differential equations of mixed type on an infinite interval in Banach spaces. We will also state an interesting example which shows that our results can apply for solving infinite systems of integro-differential equations.
关键词：measure of noncompactness ; Darbo fixed point theorem ; Arzelà-Ascoli theorem ; n th-order integro-differential equations
