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We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276{286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685{703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee's convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.


We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276{286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685{703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee's convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.