It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.

We show that if Lr(X), 1 < r < ∞, has an asymptotically uniformly convex renorming of power type then X admits a uniformly convex norm of power type.

and Applied Analysis 3 The following are some useful relationships regarding the delta derivative, see 2 . Theorem 2.6 see 2 . Assume that f : T → R and let t ∈ T. i If f is differentiable at t, then f is continuous at t. ii If f is continuous at t and t is right scattered, then f is differentiable at t with fΔ t f σ t − f t σ t − t . 2.1 iii If f is differentiable at t and t is right dense, th...

The general problem in this paper is minimizing the Cp− norm of suitable affine mappings from B(H) to Cp, using convex and differential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained charac...

We develop a general method of proving that certain star configurations in finite-dimensional normed spaces are Steiner minimal trees. This method generalizes the results of Lawlor and Morgan (1994) that could only be applied to differentiable norms. The generalization uses the subdifferential calculus from convex analysis. We apply this method to two special norms. The first norm, occurring in...

We prove a coarea-type inequality for continuously Pansu differentiable function acting between two Carnot groups endowed with homogeneous distances. assume that the level sets of are uniformly lower Ahlfors regular and differential is everywhere surjective.

In this paper we determine the number of the meaningful compositions of higher order of the differential operations and Gateaux directional derivative.

Stability results for time-varying systems with output averaged using the norm are established. The discrete-time linear system is considered under a bound on time-average on the mean-value of the output norm. It is shown that under controllability, observability and a uniform bound on the matrix norm, the time-varying system is asymptotically and uniformly stable. If, in addition, the solution...

We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of dimensionality. We show that renorming the space of infinitely differentiable functions in a suitable way allows weakly tractable uniform approximation by using only func...