On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces |
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Authors: | Ronald E Bruck |
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Institution: | (1) Department of Mathematics, University of Southern California, 90007 Los Angeles, CA, USA |
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Abstract: | We prove that ifC is a bounded closed convex subset of a uniformly convex Banach space,T:C→C is a nonlinear contraction, andS
n
=(I+T+…+T
n−1
)/n, then lim
n
‖S
n
(x)−TS
n
(x)‖=0 uniformly inx inC. T also satisfies an inequality analogous to Zarantonello’s Hilbert space inequality. which permits the study of the structure
of the weak ω-limit set of an orbit. These results are valid forB-convex spaces if some additional condition is imposed on the mapping.
Partially supported by NSF Grant MCS-7802305A01. |
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Keywords: | |
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