Rates of Asymptotic Regularity for Halpern Iterations of Nonexpansive Mappings

: In this paper we obtain new effective results on the Halpern iterations of nonexpansive mappings using methods from mathematical logic or, more specifically, proof-theoretic techniques. We give effective rates of asymptotic regularity for the Halpern iterations of nonexpansive self-mappings of nonempty convex sets in normed spaces. The paper presents another case study in the project of proof mining, which is concerned with the extraction of effective uniform bounds from (prima-facie) ineffective proofs. Key Words: Proof mining, metric fixed point theory, nonexpansive functions, asymptotic regularity, Halpern iterations. Category: G.1, F.4.1

• Type: Journal
• Year: 2007
• Where: JUCS
• Authors: Laurentiu Leustean
• Keywords: Asymptotic Regularity, Halpern Iterations, JUCS 2007, Proof Mining