A Characterization of B-convexity and J-convexity of Banach Spaces

Convexity and Geodesic Metric Spaces

In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

On difference sequence spaces defined by Orlicz functions without convexity

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.  

Curves in Banach Spaces Which Allow a C Parametrization or a Parametrization with Finite Convexity

We give a complete characterization of those f : [0, 1]→ X (where X is a Banach space) which allow an equivalent (smooth) parametrization with finite convexity, and (in the case when X has a Fréchet smooth norm) a C parametrization. For X = R, a characterization for the C case is well-known. However, even in the case X = R, several quite new ideas are needed.

ℂ-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation

We investigate the concepts of linear convexity and C-convexity in complex Banach spaces. The main result is that any C-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a C-convex domain Ω in the Banach space X and a point p / ∈Ω, there is a complex hyperplane through p that does not intersect Ω. We also prov...