We show that every quasi–norm p on a (real) cancellative cone X induces in a natural way an extended quasi–metric ep on X for which (X, ep) is an extended quasi–metric cone. We prove that the structure of a quasi– normed cone is preserved by bicompletion, under bijective isometries. In fact, we observe that isometries are not necessarily injective in this setting. Some illustrative examples are...

A basic result in semigroup theory states that every C0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e t n P ) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introd...

We prove a null space property for the uniqueness of the sparse solution vectors recovered from a minimization in `q quasi-norm subject to multiple systems of linear equations, where q ∈ (0, 1]. Furthermore, we show that the null space property for the setting of the sparse solution vectors for multiple linear systems is equivalent to the null space property for the standard minimization in `q ...

We say that the quasi-norm Φ of a symmetric sequence space E has property P if, for all x, y ∈ E with 0 ≤ xn ≤ yn for all n, and xN < yN for some N , we have Φ (xn) < Φ (yn) . Simon [6] proved that if the Banach norm Φ has property P , then whenever An → A in the weak operator topology on the unitary matrix space CE and Φ(An)→ Φ(A), then An → A in the strong operator topology on CE . In this no...

In this paper we introduce and describe two classes of aggregation functions with members that are migrative. First continuous triangular norms are studied that own the migrative property with respect to another fixed t-norm, in particular to the three prototypes minimum, product, and the Łukasiewicz t-norm. For classes of nilpotent and strict migrative t-norms the characterization and construc...

We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of b frequencies, b ≤ d + 2, in arbitrary dimension d and for arbitrary non integrable algebraic nonlinearity p. This reflects the conservation of d momenta, energy and L norm. In 1d, we prove the existence of quasi-periodic solutions with arbit...

The p-Laplacian problem is one of the typical examples of degenerate nonlinear systems arising from nonlinear diffusion and filtration, powerlaw materials and quasi-Newtonian flows. In this article we give a survey of quasi-norm techniques to establish optimal error estimates for finite element approximation of p-Laplacian.