We introduce a new class of measures of noncompactness related to asymptotic stability and ultimate monotonicity in the space of continuous and bounded functions on an unbounded interval. With help of those measures of noncompactness and a ﬁxed point theorem of Darbo type we investigate the existence of asymptotically stable and ultimately nondecreasing solutions of some quadratic functional integral equations of Hammerstein–Volterra type.
Cite this article
Jürgen Appell, Józef Banaś, Nelson Merentes, Measures of Noncompactness in the Study of Asymptotically Stable and Ultimately Nondecreasing Solutions of Integral Equations. Z. Anal. Anwend. 29 (2010), no. 3, pp. 251–273DOI 10.4171/ZAA/1408