New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces - Hayel N. Saleh; Mohammad Imdad; Thabet Abdeljawad; Mohammad Arif (Journal of Function Spaces)
In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.