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

Jürgen Appell | Zendy; Józef Banaś | Zendy; Nelson Merentes | Zendy

Open Access

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

Author(s) -

Jürgen Appell,

Józef Banaś,

Nelson Merentes

Publication year - 2010

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1408

Subject(s) - mathematics , monotonic function , fixed point theorem , interval (graph theory) , integral equation , quadratic equation , class (philosophy) , stability (learning theory) , type (biology) , bounded function , mathematical analysis , stability theory , exponential stability , space (punctuation) , combinatorics , computer science , nonlinear system , physics , quantum mechanics , ecology , geometry , artificial intelligence , machine learning , biology , operating system

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.

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