Fixed points result via $\mathcal{L}$-contractions on quasi $w$-distances
DOI:
https://doi.org/10.30495/jme.v0i0.1507Keywords:
Quasi-metric space, Fixed point, $\mathcal{L}$-contractionAbstract
The concept of a $w$-distance on a
metric space has been introduced by Kada et al. \cite{Kst}. They generalized Caristi
fixed point theorem, Ekeland variational principle and the
nonconvex minimization theorem according to Takahashi.
In the present paper, we first introduce the notion of quasi $w$-distances in quasi-metric spaces and then we will prove some fixed point theorems for $\mathcal{L}$-contractive mappings in the class of quasi-metric spaces with $w$-distances via a control function introduced by Jleli and Samet \cite{JL}. These results generalize many fixed point theorems by Kada et al. \cite{Kst}, Suzuki \cite{S}, Ciri\'{c} \cite{ciric}, Aydi et al. \cite{Aydbarlak}, Abbas and Rhoades \cite{Ar}, Kannan \cite{Kannan}, Hicks and Rhoades \cite{H}, Du \cite{D}, Lakzian et al. \cite{LAR}, Lakzian and Rhoades \cite{LR} and others. Some examples in support of the given concepts and presented results.
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