In this paper, we give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz -difference sequence space , . For this purpose, we apply the Hausdorff measure of noncompactness and use some results.

In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces `p(F̂ ) and `∞(F̂ ) to be compact, where 1 ≤ p <∞.

We construct α-Hölder continuous functions on the real line so that all their level sets have positive (1−α)-dimensional Hausdorff measure.

We consider the problem of the minimization of the p-compliance functional where the control variables Σ are taking among closed connected one-dimensional sets. we prove some estimate from below of the p-compliance functional in terms of the one-dimensional Hausdorff measure of Σ and compute the value of the constant θ(p) appearing usually in Γ-limit functional of the rescaled p-compliance func...

The compact operators on the Riesz sequence space 1 ∞ have been studied by Başarır and Kara, “IJST (2011) A4, 279-285”. In the present paper, we will characterize some classes of compact operators on the normed Riesz sequence spaces and by using the Hausdorff measure of noncompactness.

Let E ⊂ R with H(E) < ∞, where H stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit

We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity, and, under weak geodesic assumptions, they are strongly bolic as well. We show that CAT(−1) spaces are strongly hyperbolic. On the way, we determine the best ...

Following a recent paper [10] we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure H (n is interger) on a set E implies that E is rectifiable.

Bennett and Gill (1981) proved that P 6= NP relative to a random oracle A, or in other words, that the set O[P=NP] = {A | P = NP} has Lebesgue measure 0. In contrast, we show that O[P=NP] has Hausdorff dimension 1. This follows from a much more general theorem: if there is a relativizable and paddable oracle construction for a complexity-theoretic statement Φ, then the set of oracles relative t...