On existence theorems for generalized abstract measure integrodifferential equations

Abstract

In this paper, an existence and uniqueness results for a nonlinear abstract measure
integrodifferential equation are proved via classical fixed point theorems of Schauder and
Dhage \cite{Dha4} under weaker Carath\'eodory condition. The existence for extremal solutions
is also proved under certain Chandrabhan condition and using a hybrid fixed point theorem of
Dhage \cite{Dha4} in an ordered Banach space. Our existence results presented in this paper
include the existence results of Sharma \cite{RRS1}, Joshi \cite{SRJ}, Shendge and Joshi
\cite {SJ}, Dhage \cite{Dha1} and some new nonlinear abstract measure differential equations
as special cases under weaker continuity condition.