We show that the variance of a probability measure \(\mu \) on compact subset X complete metric space M is bounded by square circumradius R canonical embedding into P(M) measures M, equipped with Wasserstein metric. When barycenters are unique (such as CAT(0) spaces), our approach shows in fact coincides and so this result extends recent Lim-McCann from Euclidean space. Our involves bi-linear m...

The study of fixed points of mappings satisfying certain contractive conditions has been at the center of rigorous research activity, see 1–3 . The notion ofD-metric space is a generalization of usual metric spaces and it is introduced by Dhage 4–7 . Recently, Mustafa and Sims 8, 9 have shown that most of the results concerning Dhage’sD-metric spaces are invalid. In 8, 9 , they introduced an im...