A Nemytskii-Edelstein type fixed point theorem for partial metric spaces

被引:0
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作者
Naseer Shahzad
Oscar Valero
机构
[1] King Abdulaziz University,Department of Mathematics
[2] Universidad de las Islas Baleares,Departamento de Ciencias Matemáticas e Informática
来源
Fixed Point Theory and Applications | / 2015卷
关键词
Topological Space; Fixed Point Theorem; Contractive Condition; Cauchy Sequence; Fixed Point Theory;
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摘要
In 1994, Matthews obtained an extension of the celebrated Banach fixed point theorem to the partial metric framework (Ann. N.Y. Acad. Sci. 728:183-197, 1994). Motivated by the Matthews extension of the Banach theorem, we present a Nemytskii-Edelstein type fixed point theorem for self-mappings in partial metric spaces in such a way that the classical one can be retrieved as a particular case of our new result. We give examples which show that the assumed hypothesis in our new result cannot be weakened. Moreover, we show that our new fixed point theorem allows one to find fixed points of mappings in some cases in which the Matthews result and the classical Nemytskii-Edelstein one cannot be applied. Furthermore, we provide a negative answer to the question about whether our new result can be retrieved as a particular case of the classical Nemytskii-Edelstein one whenever the metrization technique, developed by Hitzler and Seda (Mathematical Aspects of Logic Programming Semantics, 2011), is applied to partial metric spaces.
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