Displaying similar documents to “An existence theorem for Hammerstein integral equations.”

Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (2001)

Commentationes Mathematicae Universitatis Carolinae


In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

Integrable solutions of a functional-integral equation.

Józef Banas, Zygmunt Knap (1989)

Revista Matemática de la Universidad Complutense de Madrid


This paper contains a theorem on the existence of monotonic and integrable solutions of a functional-integral equation. The proof of that theorem is based on the technique associated with the notion of a measure of weak noncompactness.