Convexity in Tree Spaces

Approximate Convexity and Submonotonicity in Locally Convex 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...

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.  

Geodesic Convexity and Cartesian Products in Graphs

In this work we investigate the behavior of various geodesic convexity parameters with respect to the Cartesian product operation for graphs. First, we show that the convex sets arising from geodesic convexity in a Cartesian product of graphs are exactly the same as the convex sets arising from the usual binary operation ⊕ for making a convexity space out of the Cartesian product of any two con...

On Some Properties of Hyperconvex Spaces

We are going to answer some open questions in the theory of hyperconvex metric spaces. We prove that in complete R-trees hyperconvex hulls are uniquely determined. Next we show that hyperconvexity of subsets of normed spaces implies their convexity if and only if the space under consideration is strictly convex. Moreover, we prove a Krein-Milman type theorem for Rtrees. Finally, we discuss a ge...