Existence theorem for the Hammerstein integral equation

• Autorzy: Mieczysław Cichoń , Ireneusz Kubiaczyk
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove an existence theorem for the Hammerstein integral equation
$x(t) = p(t) + λ ∫_I K(t,s)f(s,x(s))ds$, where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.

Słowa kluczowe

EN

integral equations; measures of weak noncompactness; Banach spaces; weak continuity

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 45N05: Abstract integral equations, integral equations in abstract spaces
• 45G10: Other nonlinear integral equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1996
• Tom: 16
• Numer: 2
• Strony: 171-177

Daty

wydano

1996

Twórcy

autor

Mieczysław Cichoń

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

autor

Ireneusz Kubiaczyk

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Bibliografia

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