کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
422603 685116 2006 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Proof Mining in R-trees and Hyperbolic Spaces
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Proof Mining in R-trees and Hyperbolic Spaces
چکیده انگلیسی

This paper is part of the general project of proof mining, developed by Kohlenbach. By "proof mining" we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs.We present logical metatheorems for general classes of spaces from functional analysis and hyperbolic geometry, like Gromov hyperbolic spaces, R-trees and uniformly convex hyperbolic spaces (in the sense of Reich/Kirk/Kohlenbach). Our theorems are adaptations to these structures of previous metatheorems of Gerhardy and Kohlenbach, and they guarantee a-priori, under very general logical conditions, the existence of uniform bounds.We give also an application in nonlinear functional analysis, more specifically in metric fixed-point theory. Thus, we show that the uniform bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in uniformly convex hyperbolic spaces obtained in a previous paper is an instance of one of our metatheorems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Electronic Notes in Theoretical Computer Science - Volume 165, 22 November 2006, Pages 95-106