… Analogues of the parallelogram identity and the (CN) inequality of Bruhat and Tits in
uniformly convex metric spaces are established. As an application of the new inequalities,
we prove two fixed point results for single-valued and multi-valued Lipschitzian mappings. …
We will say that a subset C of a hyperbolic metric space M is convex if [ x , y ] ⊂ C whenever
x , y are in C . …

… convexity in convex metric spaces, studies its properties and constructed example of a
uniformly convex metric space which is not normed space. The purpose of this paper is to
establish some inequalities in uniformly convex complete metric spaces analogous to the
parallelogram law in Hilbert spaces. Applications of the inequalities obtained to fixed points
of k-Lipschitzian involutions are also shown. …