The aim of this article to propose some generalization of Meir-Keeler
fixed point theorem with the help of an
$\alpha$-admissible mapping. Further we prove the
existence of solution of an infinite system of integral equations by
using this generalized fixed point theorem involving measure of
noncompactness in Banach space and illustrate the results with the help
of an example. Finally, apply an iterative algorithm we find an
approximate solution of an infinite system of integral equations.