Geodesic
On the fixed point theory in bicomplete quasi-metric spaces
Alegre, Carmen1 ; Dağ, Hacer2 ; Romaguera, Salvador3 ; Tirado, Pedro1
1 Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
2 Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
3 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
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5245-5251.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.009.08.10
Classification : 47H10, 54H25, 54E50
Keywords: Quasi-metric space, bicomplete, \(\varphi\)-contraction, fixed point.

Alegre, Carmen 1 ; Dağ, Hacer 2 ; Romaguera, Salvador 3 ; Tirado, Pedro 1

1 Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
2 Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
3 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 
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Alegre, Carmen; Dağ, Hacer; Romaguera, Salvador; Tirado, Pedro. On the fixed point theory in bicomplete quasi-metric spaces. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5245-5251. doi : 10.22436/jnsa.009.08.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.08.10/

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