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Nonincreasing solutions for quadratic integral equations of Convolution type

El-Sayed W. G., Abd El-Mowla A. A. H.

Journal of Mathematics and Applications

2019

Vol. 42

95--107

We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.

On nondecreasing solutions of cubic integral equations of Urysohn type

Caballero J., O’regan D., Sadarangani K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 1

39--54

Using a technique associated with measures of noncompactness we prove the existence of nondecreasing solutions to cubic integral equations of Urysohn type in C[0,1].