Nonexpansive mappings on Abelian Banach algebras and their fixed points
A Banach space X is said to have the fixed point property if for each nonexpansive mapping T : E → E 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 i...
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th-cmuir.6653943832-518162018-09-04T06:09:36Z Nonexpansive mappings on Abelian Banach algebras and their fixed points W. Fupinwong Mathematics A Banach space X is said to have the fixed point property if for each nonexpansive mapping T : E → E 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|| for each x, y ∈ X such that |τ(x)| ≤ |τ(y)| for each τ ∈ Ω(X), (iii) inf{r(x) : x ∈ X, ||x|| = 1} > 0 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). © 2012 Fupinwong; licensee Springer. 2018-09-04T06:09:36Z 2018-09-04T06:09:36Z 2012-01-01 Journal 16871812 16871820 2-s2.0-84902528913 10.1186/1687-1812-2012-150 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902528913&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51816 |
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Mathematics W. Fupinwong Nonexpansive mappings on Abelian Banach algebras and their fixed points |
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A Banach space X is said to have the fixed point property if for each nonexpansive mapping T : E → E 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|| for each x, y ∈ X such that |τ(x)| ≤ |τ(y)| for each τ ∈ Ω(X), (iii) inf{r(x) : x ∈ X, ||x|| = 1} > 0 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). © 2012 Fupinwong; licensee Springer. |
| format |
Journal |
| author |
W. Fupinwong |
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W. Fupinwong |
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W. Fupinwong |
| title |
Nonexpansive mappings on Abelian Banach algebras and their fixed points |
| title_short |
Nonexpansive mappings on Abelian Banach algebras and their fixed points |
| title_full |
Nonexpansive mappings on Abelian Banach algebras and their fixed points |
| title_fullStr |
Nonexpansive mappings on Abelian Banach algebras and their fixed points |
| title_full_unstemmed |
Nonexpansive mappings on Abelian Banach algebras and their fixed points |
| title_sort |
nonexpansive mappings on abelian banach algebras and their fixed points |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902528913&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51816 |
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