Uniformly holomorphic continuation in locally convex spaces

Locally Uniformly Convex Norms in Banach Spaces and Their Duals

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

Some Uniformly Convex Spaces

size of the éliminants but the size of their largest prime factor which is important, and secondly it is not essential to take the w's in order of magnitude. In answer, it should be pointed out that after one passes the limits of factor tables, it becomes impracticable to deal with the factors of the éliminant rather than the éliminant. Therefore, since the éliminant (in one case at least) appe...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Asymmetric locally convex spaces

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

Best Proximity Pairs in Uniformly Convex Spaces

In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using a fixed point theorem for Kakutani factorizable multi-functions.