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Introduces quasi w-distances and L-contractive fixed point theorems in quasi-metric spaces; extends prior results but leaves open applied validation.
The concept of a w-distance on a metric space has been introduced by Kada et al. {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 L-contractive mappings in the class of quasi-metric spaces with w-distances via a control function introduced by Jleli and Samet {JL}. These results generalize many fixed point theorems by Kada et al. {Kst}, Suzuki {S}, Ciri\'{c} {ciric}, Aydi et al. {Aydbarlak}, Abbas and Rhoades {Ar}, Kannan {Kannan}, Hicks and Rhoades {H}, Du {D}, Lakzian et al. {LAR}, Lakzian and Rhoades {LR} and others. Some examples in support of the given concepts and presented results.
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Barootkoob et al. (2020) studied this question.
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