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)" (Random Oper. Stoch. Equ. 15 (2007), 127-136)
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Publication Details
Author list: Kumam W., Tanutpanit T., Kumam P.
Publisher: De Gruyter
Publication year: 2008
Journal: Random Operators and Stochastic Equations (0926-6364)
Volume number: 16
Issue number: 3
Start page: 255
End page: 265
Number of pages: 11
ISSN: 0926-6364
eISSN: 1569-397X
Languages: English-Great Britain (EN-GB)
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 ∈ε Ω., T(ω,x) C 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 [13, Theorem 3.2], P. Kumam and S. Plubtieng [10, Theorem 3.2] and some other authors. Finally, a small corrigendum to the paper [13] by Wiyada Kumam and Poom Kumam is given. © de Gruyter 2008.
Keywords
Inwardness condition, Multivalued mappings, Nonstrict Opial's property, Property (D), SL-random operators
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