On the fixed point theory in bicomplete quasi-metric spaces

Volume 9, Issue 8, pp 5245--5251 http://dx.doi.org/10.22436/jnsa.009.08.10

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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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Keywords

• Quasi-metric space
• bicomplete
• \(\varphi\)-contraction
• fixed point.

MSC

•  47H10
•  54H25
•  54E50

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