Abstract. In this paper, we introduce the concept of partial cone b-metric spaces as a generalization of partial metric, cone metric and b-metric spaces and establish some topological properties of partial cone b-metric spaces. Moreover, we also prove some common fixed point theorems for cyclic contractive mappings in such spaces. Our results generalize and extend the main results of Huang and ...

Abstract We use methods from nonstandard analysis to unify and extend results the theory of asymptotic fixed points on metric spaces. Among topics we consider are Kirk’s point theorem with extensions, Boyd Wong’s theorem, Suzuki’s for contractions Meier–Keeler type. also show how final type can be modified yield uniform convergence compact bounded sets.

* Correspondence: [email protected] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Full list of author information is available at the end of the article Abstract In this paper, the existence of a fixed point for TF-contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X ® X is a one to one and closed graph...