New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces. (3rd July 2020)

• Record Type: Journal Article
• Authors: Saleh, Hayel N.; Imdad, Mohammad; Abdeljawad, Thabet; Arif, Mohammad
• Other Names: Petrusel Adrian Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-07-03
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/9491786
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.