A Kneser-type theorem for an integral equation in locally convex spaces

• Autorzy: Dutkiewicz A.
• Języki publikacji: EN

Abstrakty

EN

We shall give suffcient conditions for the existence of solutions of the integral equation (1) in locally convex spaces. We also prove that the set of these solutions is a continuum.

Słowa kluczowe

EN

convex spaces; integral equations; Kneser theorem; Banach space

PL

przestrzeń wypukła; równanie całkowe; twierdzenie Knesera; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 1
• Strony: 197--202
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Dutkiewicz A.

• Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland

Bibliografia

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• [3] J. Januszewski, On Volterra integral equations with weakly sigular kernel in Banach spaces, Demonstratio Math. 26 (1993), 131-136.
• [4] K. Kuratowski, Topologie II, New York-London-Warszawa 1968.
• [5] W. Mydlarczyk, The existence of nontrivial solutions of Volterra equations, Math. Scand. 68 (1991), 83-88.
• [6] B. N. Sadowskii, Limit-compact and condensing mappings, Russian Math. Surveys 27 (1972), 85-155.
• [7] S. Szufla, On the equation x' = f(t, x) in locally convex spaces, Math. Nachr. 118 (1984), 179-185.
• [8] S. Szufla, Sets of fixed points of nonlinear mappings in function spaces, Funkcial. Ekvac. 22 (1979), 121-126.
• [9] G. Vidossich, A fixed point theorem for function spaces, J. Math. Anal. Appl. 36 (1971), 581-587.