Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (197 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 29, Issue 3, 2010, pp. 251–273
DOI: 10.4171/ZAA/1408

Published online: 2010-06-23

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

Jürgen Appell[1], Józef Banaś[2] and Nelson Merentes[3]

(1) Universität Würzburg, Germany
(2) Rzeszów University of Technology, Poland
(3) Central University of Venezuela, Caracas, Venezuela

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.

Keywords: Measure of noncompactness, Darbo fixed point theorem, superposition operator, quadratic functional integral equation, asymptotic stability, ultimate monotonicity

Appell Jürgen, Banaś Józef, Merentes Nelson: Measures of Noncompactness in the Study of Asymptotically Stable and Ultimately Nondecreasing Solutions of Integral Equations. Z. Anal. Anwend. 29 (2010), 251-273. doi: 10.4171/ZAA/1408