Article
MSC:
26A39,
28B15,
34A36,
34A37,
45N05,
46B40,
47H07,
47H10 | MR 3010237 | Zbl 1274.45017 | DOI: 10.1007/s10492-012-0034-7
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Keywords:
integrability; Henstock-Kurzweil integral; ordered Banach space; order cone; chain; fixed point; functional integral equation; Volterra; Cauchy problem; ordered Banach space; fixed point
integrability; Henstock-Kurzweil integral; ordered Banach space; order cone; chain; fixed point; functional integral equation; Volterra; Cauchy problem; ordered Banach space; fixed point
Summary:
A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.
References:
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