eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-12-29 3 6 154 159 10.12691/tjant-3-6-3 TJANT2015363 article Tingting Guan guantingting1985@163.com 1 School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, P. R. China By using the partial order method and some new comparison results, the maximal or minimal solution of the initial value problem for nonlinear second order integro-differential equations with delayed arguments in Banach spaces are investigated. In this paper, we require only a lower solution or an upper solution and some weaker conditions presented here, and we extend and improve some recent results (see [1-11]). http://pubs.sciepub.com/tjant/3/6/3/tjant-3-6-3.pdf second-order integro-differential equation delayed arguments measure of non-compactness solution monotone iterative technique