This study is devoted to investigate the problem whether existence and uniqueness of integral type contraction mappings on orthogonal metric spaces. At end, we give an example illustrative our main result.

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

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...