JournalszaaVol. 29, No. 3pp. 251–273

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

  • Jürgen Appell

    Universität Würzburg, Germany
  • Józef Banaś

    Rzeszów University of Technology, Poland
  • Nelson Merentes

    Central University of Venezuela, Caracas, Venezuela
Measures of Noncompactness in the Study of Asymptotically Stable and Ultimately Nondecreasing Solutions of Integral Equations cover
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Abstract

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. 251–273

DOI 10.4171/ZAA/1408