A remark on some random fixed points of multivalued SL-random operators satisfying the nonstrict Opial's property and corrigendum to “Random fixed points of multivalued random operators with property (D)”
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Wiyada Kumam
Abstract
Let C be a nonempty closed bounded convex separable subset of a reflexive Banach space X satisfying the nonstrict Opial's property and property (D) which was introduced by Dhompongsa et al. (2006). If T : Ω × C → KC(X) is an SL-random operator that satisfies the inwardness condition, i.e., for each ω ∈ Ω, T(ω, x) ⊂ Ic(x), ∀x ∈ C, then T has a random fixed point. Our result is an extension of some results given by W. Kumam and P. Kumam in [Random Oper. Stoch. Equ. 15: 127–136, 2007, Theorem 3.2], P. Kumam and S. Plubtieng [Random Oper. Stoch. Equ. 14: 35–44, 2006, Theorem 3.2] and some other authors. Finally, a small corrigendum to the paper [Random Oper. Stoch. Equ. 15: 127–136, 2007] by Wiyada Kumam and Poom Kumam is given.
© de Gruyter 2008
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Articles in the same Issue
- Weak solutions for random nonlinear parabolic equations of nonlocal type
- A simplified version of Cochran's theorem in mixed linear models
- On a method for an effective calculation of optimal estimates in problems of a filtration of random processes for certain nonlinear evolution differential equations in a Hilbert space. Part 1
- A remark on some random fixed points of multivalued SL-random operators satisfying the nonstrict Opial's property and corrigendum to “Random fixed points of multivalued random operators with property (D)”
- Discrete time approximation of BSDEs driven by a Lévy process
- Transforming random operators into random bounded operators
- A remark on probability distributions and characteristic functionals for random functions of sets
