Abstract: Let K be a closed convex subset of a real reflexive Banach space E, T:K→K be a nonexpansive mapping, and f:K→K be a fixed weakly contractive (may not be contractive) mapping. Then for any t∈(0, 1), let x_t(K be the unique fixed point of the weak contraction x↦tf(x)+(1−t)Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^*, then it is shown that {x_t} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in (Xu, 2004).

Key words: Viscosity approximation methods, Weakly contractive mapping, Fixed point, Weakly sequentially continuous duality mapping

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