On the Volterra integral equation and axiomatic measures of weak noncompactness. (English) Zbl 0982.45002

Bugajewski, Dariusz

Math. Bohem. 126, No. 1, 183-190 (2001).

Summary: We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.

MSC:

45G10	Other nonlinear integral equations
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

measure of weak noncompactness; nonlinear Volterra integral equation; Kneser property