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Generic power convergence of operators in banach spaces |
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| Authors: | Dan Butnariu Simeon Reich Alexander J. Zaslavski |
| Affiliation: | 1. Department Of Mathematics , University Of Haifa , 31905 Haifa, DB, Israel;2. Department Of Mathematics , The Technion-Israel Institute Of Technology , 32000 Haifa, Sr And Ajz, Israel E-mail: dbutnaru@mathcs2.haifa.ac.il;3. sreich@tx.technion.ac.il;4. ajzasl@tx.technion.ac.il |
| Abstract: | Let K be a closed convex subset of a Banach space X. We consider complete metric spaces of self-mappings of K which are nonexpansive with respect to a convex function on X. We prove that the iterates of a generic operator in these spaces converge strongly. In some cases the limits do not depend on the initial points and are the unique fixed point of the operator. |
| Keywords: | Bregman distance convex function fixed point generic property iterative algorithm uniform space 49M30 52A41 58F99 |