Preliminaries on CAT (0) Spaces and Fixed Points of a Class of Iterative   Schemes
  This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some properties of uniform convexity and near uniform convexity of geodesic metric spaces are related to the mapping built with the concourse of two primary mappings and the associated generated sequences by some iterative schemes. 
M De la Sen
math.FA