Random fixed point theorems for multivalued subsequentially limit-contractive maps satisfying inwardness conditions
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Author list: Kumam W., Kumam P.
Publisher: Eudoxus Press LLC
Publication year: 2012
Journal: Journal of Computational Analysis and Applications (1521-1398)
Volume number: 14
Issue number: 2
Start page: 239
End page: 251
Number of pages: 13
ISSN: 1521-1398
Languages: English-Great Britain (EN-GB)
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Abstract
Let (Ω, ∑) be a measurable space, with ∑ a sigma-algebra of subset of Ω; and let C be a non-empty bounded closed convex and separable subset of a Banach space X; satisfying property (D), KC(X) the family of all compact convex subsets of X: We prove that a continuous 1-χ contrac-tive mutivalued subsequentially limit-contractive map from C into KC(X) satisfying an inwardness condition has a random [Fixed point. Our work also extends and improves stochastic version of the results of Shahzad and Lone [Fixed point of multimaps which are not necessarily nonexpansive, Fixed Point Theory Applications, 2 (2005), 169-176] and connected with Khan and Domlo, [Random fixed points of multivalued inward random operators, Journal of Applied Mathematics and Stochastic Analysis, Volume 2006 (2006), Article ID 19428, 8 pages], Plubtieng and Kumam [Random fixed point theorems for multivalued nonexpansive non-selfrandom operators, Journal of Applied Mathe-matics and Stochastic Analysis, 2006 (2006), Article ID 43796, 9 pages]. © 2012 EUDOXUS PRESS, LLC.
Keywords
Dominguez-lorenzo condition, SL maps
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