The hierarchy of the block bases of transfinite normalized averages of a normalized Schauder basic sequence is introduced and a criterion is given for a normalized weakly null sequence in C(K), the Ba-nach space of scalar valued functions continuous on the compact metric space K, to admit a block basis of normalized averages equivalent to the unit vector basis of c0, the Banach space of null sc...

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

Recently, Rahimi et al. [Comp. Appl. Math. 2013, In press] defined the concept of quadrupled fied point in K-metric spaces and proved several quadrupled fixed point theorems for solid cones on K-metric spaces. In this paper some quadrupled fixed point results for T-contraction on K-metric spaces without normality condition are proved. Obtained results extend and generalize well-known comparable...

let (x, d) be a compact metric space and f : x → x be a continuous map. consider the metric space (k(x),h) of all non empty compact subsets of x endowed with the hausdorff metric induced by d. let ¯ f : k(x) → k(x) be defined by ¯ f(a) = {f(a) : a ∈ a} . we show that block-coppels chaos in f implies block-coppels chaos in ¯ f if f is a bijection.

in this paper, we generalize fuzzy banach contraction theorem establishedby v. gregori and a. sapena [fuzzy sets and systems 125 (2002) 245-252]using notion of altering distance which was initiated by khan et al. [bull. austral.math. soc., 30(1984), 1-9] in metric spaces.

a set $wsubseteq v(g)$ is called a resolving set for $g$, if for each two distinct vertices $u,vin v(g)$ there exists $win w$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. the minimum cardinality of a resolving set for $g$ is called the metric dimension of $g$, and denoted by $dim(g)$. in this paper, it is proved that in a connected graph $...

Research during the last several decades indicates the failure of existing nutritional labels to substantially improve the healthfulness of consumers' food/beverage choices. The present study aims to fill this void by developing a nutrition metric that is more comprehensible to the average shopper. The healthfulness ratings of 205 sample foods/beverages by leading nutrition experts formed the b...

We present a framework for the modeling of multipath routing in connectionless networks that dynamically adapt to network congestion. The basic routing protocol uses a short-term metric based on hop-by-hop credits to reduce congestion over a given link, and a long-term metric based on end-to-end path delay to reduce delays from a source to a given destination. A worst-case bound on the end-to-e...