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**1 - 3**of**3**### EFFECTIVE ASYMPTOTIC REGULARITY FOR ONE-PARAMETER NONEXPANSIVE SEMIGROUPS

"... Abstract. We give explicit bounds on the computation of approximate com-mon fixed points of one-parameter strongly continuous semigroups of nonex-pansive mappings on a subset C of a general Banach space. Moreover, we provide the first explicit and highly uniform rate of convergence for an itera-tive ..."

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Abstract. We give explicit bounds on the computation of approximate com-mon fixed points of one-parameter strongly continuous semigroups of nonex-pansive mappings on a subset C of a general Banach space. Moreover, we provide the first explicit and highly uniform rate of convergence for an itera-tive procedure to compute such points for convex C. Our results are obtained by a logical analysis of the proof (proof mining) of a theorem by T. Suzuki.

### Effective results on compositions of nonexpansive mappings

, 2014

"... This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We ob-tain our quantitative results in the setting of (r, δ)-convex spaces, a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombi ..."

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This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We ob-tain our quantitative results in the setting of (r, δ)-convex spaces, a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombing. MSC: 47J25; 47H09; 53C23; 03F10.