Abstract:

 By using a new established comparison result and the Mnch fixed point theorem, the existence of solutions of initial value problems for nonlinear second order intergro-differential equations of mixed type in Banach spaces is investigated. Also, one sufficient condition for the existence of minimal and maximal solutions is obtained through applying the  measure of noncompactness. The results improve and generalize some well-known results.

Key words:  integro-differential equations; initial value problems; comparison result; measure of noncompactness