Fixed point theorems for $\Theta$-contractions in left $K$-complete $T_{1}$-quasi metric space

Lateef, Durdana ¹ ; Ahmad, Jamshaid ²

¹ Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia
² Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia

Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 10, p. 667-674.

Résumé

The aim of this paper is to define $\Theta _{\beta }^{u}=\left \{ v\in \mathcal{J}u:\Theta (\varrho (u,v))\leq \lbrack \Theta (\varrho (u,\mathcal{J}u))]^{\beta }\right \} $ and establish some new fixed point theorems in the setting of left $K$-complete $T_{1}$-quasi metric space. Our theorems generalize, extend, and unify several results of literature.

Détail

DOI : 10.22436/jnsa.012.10.05

Classification : 47H10, 54H25
Keywords: \(\Theta\)-contractions, property \(P\), property \(Q\), fixed points

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