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

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)].


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


Zbl 0911.47057
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