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...

1. INTRODUCTION. When studying a metric space, it is valuable to have a mental picture that displays distance accurately. When the space is Z, Q, or R, we usually form such a picture by imagining points on the " number line ". When the space is X = Z 2 , Q 2 , R 2 , or C we use a planar picture in which nonempty discs (sets of the form {x ∈ X : d(x, b) ≤ γ } or {x ∈ X : d(x, b) < β}, with metri...

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...

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.