Commuting contractive families

• Autorzy: Luka Milićević
• Języki publikacji: EN

Abstrakty

EN

A family f₁,..., fₙ of operators on a complete metric space X is called contractive if there exists a positive λ < 1 such that for any x,y in X we have $d(f_i(x),f_i(y)) ≤ λ d(x,y)$ for some i. Austin conjectured that any commuting contractive family of operators has a common fixed point, and he proved this for the case of two operators. We show that Austin's conjecture is true for three operators, provided that λ is sufficiently small.

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 54E50: Complete metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 231
• Numer: 3
• Strony: 225-272

Daty

wydano

2015

Twórcy

autor

Luka Milićević

• Trinity College, Cambridge CB2 1TQ, United Kingdom

Identyfikatory

DOI

10.4064/fm231-3-2