TY - JOUR AU - Allahyari, Reza AU - Arab, Reza AU - Haghighi, Ali Shole PY - 2015 DA - 2015/12/15 TI - Construction of measures of noncompactness of $\mathit{DC}^{n}[J,E]$and $C^{n}_{0}[J,E]$with application to the solvability of nth-order integro-differential equations in Banach spaces JO - Advances in Difference Equations SP - 376 VL - 2015 IS - 1 AB - In the present paper, we first investigate the construction of compact sets of $\mathit{DC}^{n}[J,E]$and $C^{n}_{0}[J,E]$, 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. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-015-0718-x DO - 10.1186/s13662-015-0718-x ID - Allahyari2015 ER -