On the fixed point theory in bicomplete quasi-metric spaces
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Authors
Carmen Alegre
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.
Hacer Dağ
- Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.
Salvador Romaguera
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.
- Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.
Pedro Tirado
- Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain.
Abstract
We show that some important fixed point theorems on complete metric spaces as Browder's fixed point
theorem and Matkowski's fixed point theorem can be easily generalized to the framework of bicomplete
quasi-metric spaces. From these generalizations we deduce quasi-metric versions of well-known fixed point
theorems due to Krasnoselskiĭ and Stetsenko; Khan, Swalesh and Sessa; and Dutta and Choudhury, respectively. In fact, our approach shows that many fixed point theorems for \(\varphi\)-contractions on bicomplete
quasi-metric spaces, and hence on complete G-metric spaces, are actually consequences of the corresponding
fixed point theorems for complete metric spaces.
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ISRP Style
Carmen Alegre, Hacer Dağ, Salvador Romaguera, Pedro Tirado, On the fixed point theory in bicomplete quasi-metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 8, 5245--5251
AMA Style
Alegre Carmen, Dağ Hacer, Romaguera Salvador, Tirado Pedro, On the fixed point theory in bicomplete quasi-metric spaces. J. Nonlinear Sci. Appl. (2016); 9(8):5245--5251
Chicago/Turabian Style
Alegre, Carmen, Dağ, Hacer, Romaguera, Salvador, Tirado, Pedro. "On the fixed point theory in bicomplete quasi-metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 8 (2016): 5245--5251
Keywords
- Quasi-metric space
- bicomplete
- \(\varphi\)-contraction
- fixed point.
MSC
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