Very recently, the notion of extended 𝑏-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended 𝑏-metric space is given.
Aydi, Hassen; Felhi, Abdelbasset; Kamran, Tayyab; Karapınar, Erdal; and Ali, Muhammad U.
On Nonlinear Contractions in New Extended 𝒃-Metric Spaces,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
1, Article 37.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss1/37