In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

A topological group G is defined to have property (OB) if any G-action by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of strong uncountable cofinality in the context of Polish groups, where we show it to have several interesting reformulations and consequences. We subsequently apply the results obtained in order to verify ...

recently, cho et al. [y. j. cho, r. saadati, s. h. wang, common xed point theorems on generalized distance in ordered cone metric spaces, comput. math. appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. in this paper, we prove some new xed point and common xed point theorems by using the distance in ordere...

An M-space is a metric space (X, d) having the property that for each pair of points p, q ∈ X with d(p, q) = λ and for each real number α ∈ [0, λ], there is a unique rα ∈ X such that d(p, rα) = α and d(rα, q) = λ − α. In an M-space (X, d), we say that metric segments have unique prolongations if points p, q, r, s satisfy d(p, q) + d(q, r) = d(p, r), d(p, q) + d(q, s) = d(p, s) and d(q, r) = d(q...

In this paper we define weak $F$-contractions on a‎ ‎metric space into itself by extending $F$-contractions‎ ‎introduced by D‎. ‎Wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎Some relationships between weak‎ ‎$F$-contractions and $Fi$-contractions are highlighted‎. ‎We also ‎give some application...

Recently, Cho et al. [Y. J. Cho, R. Saadati, S. H. Wang, Common xed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] dened the concept of the c-distance in a cone metric space and proved some xed point theorems on c-distance. In this paper, we prove some new xed point and common xed point theorems by using the distance in ordered con...

Let (X; ) be a metric space, let (K(X); e ) denote the space of nonempty compact subsets of X with the Hausdor metric, and let E X. The purpose of this paper is to investigate the relationships between the entropy dimensions of E and of K(E). 1 The de nition and properties of the entropy indices. Given a separable metric space (X; ), let K(X) denote the set of non-empty compact subsets of X . D...