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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.

Measures of Noncompactness in the Study of Asymptotically Stable and Ultimately Nondecreasing Solutions of Integral Equations