Fixed Point Results via L-Contractions on Quasi w-Distances

The concept of a w-distance on a metric space has been introduced by Kada et al. [22]. They generalized Caristi xed point theorem, Ekeland variational principle and the nonconvex minimiza- tion theorem according to Takahashi. In the present paper, we rst introduce the notion of quasi w-distances in quasi-metric spaces, and then we will prove some xed point theorems for L-contractive map- pings in the class of quasi-metric spaces with w-distances via a control function introduced by Jleli and Samet [20]. These results generalize many xed point theorems by Kada et al. [22], Suzuki [33], Ciric [15], Aydi et al. [6], Abbas and Rhoades [1], Kannan [23], Hicks and Rhoades [19], Du [16], Lakzian et al. [26], Lakzian and Rhoades [30] and others. Finally, some examples in support of the concepts and presented results are given.