Fixed point theorems of order-Lipschitz mappings in Banach algebras

In this paper, by introducing the concept of Picard-completeness and using the sandwich theorem in the sense of w -convergence, we first prove some fixed point theorems of order-Lipschitz mappings in Banach algebras with non-normal cones which improve the result of Sun’s since the normality of the c...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering 2016-12, Vol.2016 (1), p.1-10, Article 30
Main Authors: Jiang, Shujun, Li, Zhilong
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Cones
Differential Geometry
Fixed points (mathematics)
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Normality
Spectra
Sun
Theorems
Topology
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Summary:In this paper, by introducing the concept of Picard-completeness and using the sandwich theorem in the sense of w -convergence, we first prove some fixed point theorems of order-Lipschitz mappings in Banach algebras with non-normal cones which improve the result of Sun’s since the normality of the cone was removed. Moreover, we reconsider the case with normal cones and obtain a fixed point theorem under the assumption relating to the spectral radius, which partially improves the results of Krasnoselskii and Zabreiko’s. In addition, we present some suitable examples which show the usability of our theorems.
ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-016-0519-2