Iterative Approximation of Fixed Points of Lipschitz Pseudocontractive Maps
نویسندگان
چکیده
Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., `p, 1 < p < ∞). Let T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K of E and let ω ∈ K be arbitrary. Then the iteration sequence {zn} defined by z0 ∈ K, zn+1 = (1 − μn+1)ω + μn+1yn; yn = (1 − αn)zn + αnTzn, converges strongly to a fixed point of T , provided that {μn} and {αn} have certain properties. If E is a Hilbert space, then {zn} converges strongly to the unique fixed point of T closest to ω.
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