In this paper, we give some new definitions of M-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete M-fuzzy metric spaces.

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...

The Work Function Algorithm, a natural algorithm for the k-server problem, is shown to have competitive ratio at most 2k− 1 for all metric spaces. It is also shown that the k-server conjecture, which states that there is an on-line algorithm for the k-server problem with competitive ratio k, holds for all metric spaces with k + 2 points. Furthermore, two refinements of competitive analysis are ...

Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric measure space into k clusters, minimizing some objective function f . Sketching, on the other hand, is the problem of approximating some metric measure space by a smaller one supported on a set of k points. Specifically...

Recently, Choudhury and Metiya [Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of the Banach's contraction mapping, which have been studied by several authors. In this paper, we introduce the notion of $f$-weak contractions and als...

In this paper, we define the concept of compatible and weakly compatible mappings in b-metric spaces and inspired by the Ciric and et. al method, we produce appropriate conditions for given the unique common fixed point for a family of the even number of self-maps with together another two self-maps in a complete b-metric spaces. Also, we generalize this common fixed point theorem for a seq...

in this paper, we prove some common fixed point results for two self mappingsf and g on s-metric space such that f is a g.w.c.m with respect to g.

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...

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...