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In this paper we apply methods of proof mining to obtain a highly uniformeffective rate of asymptotic regularity for the Ishikawa iteration associatedto nonexpansive self-mappings of convex subsets of a class of uniformly convexgeodesic spaces. Moreover, we show that these results are guaranteed by acombination of logical metatheorems for classical and semi-intuitionisticsystems.

An application of proof mining to nonlinear iterations