In this paper we extend complex uniform convexity estimates for $\mathbb{C}$ to $\mathbb{R}^n$ and determine best constants. Furthermore, provide the link log-Sobolev inequalities hypercontractivity ultraspherical measures.

Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...

The aim of this paper is to present some existence results for nearest-point and farthestpoint problems, in connection with some geometric properties of Banach spaces. The idea goes back to Efimov and Stečkin who, in a series of papers (see [28, 29, 30, 31]), realized for the first time that some geometric properties of Banach spaces, such as strict convexity, uniform convexity, reflexivity, an...

We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting syste...

Recently, in [4] the author has proved that if B is an open unit ball in a Cartesian product l2× l2 furnished with the lp-norm ‖ · ‖ and kB is the Kobayashi distance on B, then the metric space (B,kB) is locally uniformly linearly convex. In this paper, we introduce this kind of local uniform convexity in bounded convex domains in complex reflexive Banach spaces and we apply this notion in the ...

This paper focuses on the numerical analysis of a nonconvex variational problem which is related to the relaxation of the two-well problem in the analysis of solid-solid phase transitions with incompatible wells and dependence on the linear strain in two dimensions. The proposed approach is based on the search for minimizers for this functional in finite element spaces with Courant elements and...