Extension of the Fisher theorem

In this paper, we extend the Fisher fixed point theorem for a pair of mappings on metric space to maps on a complete cone metric space that satisfy the contractive condition of Perov type. This kind of contractive condition includes, instead of the contractive constant, an increasing bounded linear...

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Bibliographic Details
Published in:Mathematical proceedings of the Royal Irish Academy 2016-01, Vol.116A (1), p.71-82
Main Authors: Marija Cvetković, Erdal Karapinar, Vladimir Rakočević
Format: Article
Language:English
Subjects:
Banach space
College mathematics
Diagonal lemma
Linear transformations
Mathematical constants
Mathematical theorems
Online Access:Get full text
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Summary:In this paper, we extend the Fisher fixed point theorem for a pair of mappings on metric space to maps on a complete cone metric space that satisfy the contractive condition of Perov type. This kind of contractive condition includes, instead of the contractive constant, an increasing bounded linear operator with spectral radius less than one. The obtained results do not require a normality condition. The presented results could not be derived from Fisher's results by the scalarisation method of Du [7].
ISSN:1393-7197
2009-0021
DOI:10.3318/PRIA.2016.116.06