Abstract
In this manuscript, we utilize the concept of modified -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified -distance on quasi metric spaces and fixed point theorems on complete quasi metric spaces. Topol. Appl. 2016, 203, 120-129] in 2016 to introduce the notions of -Suzuki contraction and generalized -Suzuki contraction. We employ these notions to prove some fixed point results. Moreover, we introduce an example to show the novelty of our results. Furthermore, we introduce some applications for our results.