A sufficient condition for the existence of monotone solutions of the following nonlinear quadratic integral equation of Volterra type
is established. The approach is based on Darbo’s fixed point theorem and the measure of noncompactness introduced by J. Banaś and L. Olszowy [in Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 41, 13–23 (2001; Zbl 0999.47041)].