Iterative Methods for Fixed Points of Asymptotically Weakly Contractive Maps |
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Authors: | R.P. Gilbert C.E. Chidume H. Zegeye ? S.J. Aneke ? |
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Affiliation: | 1. The Abdus Salam International Center for Theoretical Physics , Strada Constiesa II , 34100 , Trieste , Italy chidume@ictp.trieste.it;3. The Abdus Salam International Center for Theoretical Physics , Strada Constiesa II , 34100 , Trieste , Italy |
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Abstract: | Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : K → E is an asymptotically d-weakly contractive map with sequence {kn }, kn ≥ 1, lim kn = 1 and with F(T) n int (K) ≠ ø F(T):= {x ∈ K: Tx = x}. Suppose {x n } is iteratively defined by x n+1 = P((l ? knαn )x n +k n α n T(PT) n?l xn ), n = 1,2,...,x 1 ∈ K, where αn∈ (0,l) satisfies lim αn = 0 and Σαn = ∞. It is proved that {x n } converges strongly to some x * ∈ F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {xn } converges strongly to some x * ∈ F(T). |
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Keywords: | Asymptotically d-weakly contractive d-Weakly contractive Weakly contractive Nonexpansive retraction |
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