Nonexpansive mappings on Abelian Banach algebras and their fixed pointsReportar como inadecuado




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Fixed Point Theory and Applications

, 2012:150

Professor Anthony To-Ming Lau-s contributions to the development of Fixed Point Theory and Applications.

Abstract

A Banach space X is said to have the fixed point property if for each nonexpansive mapping T : E → E Open image in new window on a bounded closed convex subset E of X has a fixed point. We show that each infinite dimensional Abelian complex Banach algebra X satisfying: i property A defined in Fupinwong and Dhompongsa in Fixed Point Theory Appl. 2010:Article ID 34959, 2010, ii ∥ x ∥ ≤ ∥ y ∥ Open image in new window for each x , y ∈ X Open image in new window such that | τ x | ≤ | τ y | Open image in new window for each τ ∈ Ω X Open image in new window, iii inf { r x : x ∈ X , ∥ x ∥ = 1 } > 0 Open image in new window does not have the fixed point property. This result is a generalization of Theorem 4.3 in Fupinwong and Dhompongsa in Fixed Point Theory Appl. 2010:Article ID 34959, 2010.

MSC: 46B20, 46J99.

Keywordsfixed point property nonexpansive mapping Abelian Banach algebra  Download fulltext PDF



Autor: W Fupinwong

Fuente: https://link.springer.com/







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