New contractive mappings and their fixed points in Branciari metric spaces (Q780090)

Summary: In this paper, we introduce the notion of generalized \(\mathcal{L}\)-contractions which enlarge the class of \(\mathcal{L}\)-contractions initiated by \textit{S.-H. Cho} [Abstr. Appl. Anal. 2018, Article ID 1327691, 6 p. (2018; Zbl 1470.54052)]. Thereafter, we also, define the notion of \(\mathcal{L}^\ast\)-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.