A GENERALIZATION AND APPLICATION OF ASCOLI-ARZELA THEOREM
Ascoli-Arzela定理的一个推广及应用

In this paper the sufficient condition and necessary condition are given for relative compactness of a class of abstract continuous function groups. By applying them, we prove the existence of solutions of terminal value problems for nonlinear first order differential equation and solutions for Fredholm integro-equation in Banach spaces.