In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

In 2007, Long-Guang and Xian[3] replaced introduced cone metric spaces. They replaced the set of real numbers by an ordered Banach space in the definition of metric and generalized the notion of metric space. Recently, Ayse Sönemaz [5] proved a cone metric space with a normal cone, of course it has to be strongly minihedral, is paracompact. In this paper we omit the strongly minihedral of cone....

‎recently‎, ‎hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎in this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎these results generalize a result of feng and liu on multi-valued operators.

in this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by gregori and sapena [v. gregori, a. sapena, on xed-point the- orems in fuzzy metric spaces, fuzzy sets and systems, 125 (2002), 245-252].

In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

In this note, we prove common fixed point for a Banach pair of mappings on D∗-Generalized Cone Metric Space.

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Abstract Berinde and Borcut (Nonlinear Anal. 74(15):4889-4897, 2011) have quite recently defined the notion of a triple fixed point and proved some interesting results related to this concept in a partially ordered metric space. In this wor...

The concept of a 2-metric space is a natural generalization of a metric space. It has been investigated initially by Gähler [4]. Iseki [5] studied the fixed point theorems in 2-metric spaces. Sessa [17] defined weak commutativity and proved common fixed point theorem for weakly commuting maps. In [7] Jungck introduced more generalized commuting mappings, called compatible mappings, which are mo...

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...