Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
1991 ◽
Vol 43
(1)
◽
pp. 153-159
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Keyword(s):
Let T be an asymptotically nonexpansive self-mapping of a closed bounded and convex subset of a uniformly convex Banach space which satisfies Opial's condition. It is shown that, under certain assumptions, the sequence given by xn+1 = αnTn(xn) + (1 - αn)xn converges weakly to some fixed point of T. In arbitrary uniformly convex Banach spaces similar results are obtained concerning the strong convergence of (xn) to a fixed point of T, provided T possesses a compact iterate or satisfies a Frum-Ketkov condition of the fourth kind.
2020 ◽
Vol 2020
◽
pp. 1-9
◽
1994 ◽
Vol 124
(1)
◽
pp. 23-31
2006 ◽
Vol 74
(1)
◽
pp. 143-151
◽
2021 ◽