Fixed points and stability of an integral equation: Nonuniqueness

We consider a paper of Banas and Rzepka which deals with existence and asymptotic stability of an integral equation by means of fixed-point theory and measures of noncompactness. By choosing a different fixed-point theorem, we show that the measures of noncompactness can be avoided and the existence and stability can be proved under weaker conditions. Moreover, we show that this is actually a problem about a bound on the behavior of a nonunique solution. In fact, without nonuniqueness, the theorems of stability are vacuous. (C) 2004 Elsevier Ltd. All rights reserved.