We consider the concept of fuzzy quasi-contractions initiated by '{C}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{H}$-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani.The results are illustrated by a representative example.

A median of a k-tuple =(x1; : : : ; xk) of elements of a 0nite metric space (X; d) is an element x for which ∑k i=1 d(x; xi) is minimum. The function m with domain the set of all k-tuples with k ¿ 0 and de0ned by m( ) = {x: x is a median of } is called the median function on X . Continuing with the program of characterizing m on various metric spaces, this paper presents a characterization of t...

We study approximation algorithms for k-median clustering. We obtain small coresets for k-median clustering in metric spaces as well as in Euclidean spaces. Specifically, in IR, those coresets are of size with only polynomial dependency on d. This leads to a (1 + ε)-approximation algorithm for kmedian clustering in IR, with running time O(ndk + 2 O(1) dn), for any σ > 0. This is an improvement ...

This paper studies space bounded algorithms, i.e., algorithms that use a constant amount of scratch space, for the k{server problem. The paper rst shows a characterization of the set of space bounded algorithms that are competitive in nite metric spaces. The result yields a method for (1) e ectively deciding if a given space bounded algorithm is competitive in a given nite metric space, and (2)...

In prior work [4] of the first two authors with Savaré, a new Riemannian notion of lower bound for Ricci curvature in the class of metric measure spaces (X, d,m) was introduced, and the corresponding class of spaces denoted by RCD(K,∞). This notion relates the CD(K,N) theory of Sturm and Lott-Villani, in the case N = ∞, to the Bakry-Emery approach. In [4] the RCD(K,∞) property is defined in thr...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

In this paper, some recent results established by Marin Borcut [M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207--214] and [M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...

In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.