Fixed point theorems for weakly sequentially closed maps. (English) Zbl 1049.47051

O’Regan, Donal

Arch. Math., Brno 36, No. 1, 61-70 (2000).

The author continues his investigation of the solvability of the abstract operator inclusion \(y(t)\in F\, y(t)\) in a Banach space, where \(F:Q\to CK(C)\), \(Q,C\) being closed, bounded and convex subsets of a Banach space, and \(CK(C)\) denotes the family of nonempty, convex, weakly compact subsets of \(C\). A number of fixed point theorems is presented and the obtained results are applied to the investigation of solvability of a class of differential inclusions in Banach spaces. The author’s related results are D. O’Regan [Math. Comput. Modelling 27, No. 5, 1–14 (1998; MR 99c:47092)] and D. O’Regan [Z. Anal. Anwend. 17, No. 5, 281–296 (1998; Zbl 0911.47057)].

Reviewer: Ondřej Došlý (Brno)

MSC:

47H10	Fixed-point theorems
47J05	Equations involving nonlinear operators (general)

Keywords:

fixed points; weakly sequentially closed maps; weakly contractive maps

Citations:

Zbl 0911.47057