hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

In this article we survey the existence of best proximity points for a class of non-self mappings which‎ satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [‎A‎. ‎Abkar‎, ‎M‎. ‎Gabeleh‎, Best proximity points of non-self mappings‎, ‎Top‎, ‎21, (2013)‎, ‎287-295]‎ which guarantees the existence of best proximity points for nonex...

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...

Geometry of Fisher metric and geodesics on a space of probability measures defined on a compact manifold is discussed and is applied to geometry of a barycenter map associated with Busemann function on an Hadamard manifold X . We obtain an explicit formula of geodesic and then several theorems on geodesics, one of which asserts that any two probability measures can be joined by a unique geodesi...

In this work we study the issue of geodesic extendibility on complete and locally compact metric length spaces. We focus geometric structure space $(\Sigma (X),d_H)$ balls endowed with Hausdorff distance give an explicit isometry between closed half-space $ X\times \mathbb{R}_{\ge 0}$ a taxicab metric. Among applications establish group $\mbox{Iso} (X,d)$ (\Sigma when $(X,d)$ is Hadamard space.

We study the Steiner problem of finding a minimal spanning network in the setting of a space of probability measures with metric defined by cost of optimal transport between measures. Existence of a solution is shown for the Wasserstein space Pp(X ) over any base space X which is a separable, locally compact Hadamard space. Structural results are given for the case p = 2 under further restricti...