Effective metastability of Halpern iterates in CAT(0) spaces

Details Effective metastability of Halpern iterates in CAT(0) spaces Effective metastability of Halpern iterates in CAT(0) spaces

2011-07-16

arxiv.org/abs/1107.3215v3

Mathematics

Functional Analysis

some typos corrected; acknowledgements added

Scientific paper

This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction of this rate from an ineffective proof due to Saejung is an instance of the general proof mining program which uses tools from mathematical logic to uncover hidden computational content from proofs. This methodology is applied here for the first time to a proof that uses Banach limits and hence makes a substantial reference to the axiom of choice.

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