In this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in $C[I, E]$, where $E$ is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.
"Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations." Nagoya Math. J. 158 73 - 86, 2000.