For a (compact) subset K of a metric space and ε > 0, the covering number N(K, ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In t...

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...

Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...

For any countable CW -complex K and a cardinal number τ ≥ ω we construct a completely metrizable space X(K, τ) of weight τ with the following properties: e-dimX(K, τ) ≤ K, X(K, τ) is an absolute extensor for all normal spaces Y with e-dimY ≤ K, and for any completely metrizable space Z of weight ≤ τ and e-dimZ ≤ K the set of closed embeddings Z → X(K, τ) is dense in the space C(Z,X(K, τ)) of al...

in this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. our results generalize kannan and chatterjea fixed point theorems on complete $b$-metric spaces. in particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. we also give some examples to illustrate the given results.

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...

We survey work of Lott-Villani and Sturm on lower Ricci curvature bounds for metric-measure spaces. An intriguing question is whether one can extend notions of smooth Riemannian geometry to general metric spaces. Besides the inherent interest, such extensions sometimes allow one to prove results about smooth Riemannian manifolds, using compactness theorems. There is a good notion of a metric sp...

In a normed linear space X, consider a nonempty closed set K which has the property that for some r > 0 there exists a set of points xo € X\K, d(xoK) > r, which have closest points p(xo) € K and where the set of points xo — r((xo — p(xo))/\\xo — p(zo)||) is dense in X\K. If the norm has sufficiently strong differentiability properties, then the distance function d generated by K has similar dif...

The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of C for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely, E k(f,X) (−→ 1/k, f,X ) , where E k(f,X) is the deviation of the best approximation of f ∈ X by polynomials of degree at most kj about the jth variable zj with respect to the X-metric and ...

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...