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Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

โœ Scribed by Hossein Dehghan

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
213 KB
Volume
24
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [S. Matsushita, W. Takahashi, Approximating fixed points of nonexpansive mappings in a Banach space by metric projections, Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.

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Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K โ†’ E be a nonexpansive non-self map with n 1, where { n } and { n } are real sequences in [ , 1 -] for some โˆˆ (0, 1). ( 1) If the dual E \* of E has the