in this paper, we deal with the subdi erential 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 subdi erentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdi erential set is established.
In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and suficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spac
and Applied Analysis 3 Theorem 2.1 Kirk 1 . LetU be a bounded open subset of a Hadamard space X and S : clU → X a nonexpansive mapping. Suppose that there exists p ∈ U such that every x in the boundary ofU does not belong to p, Sx \ {Sx}. Then, S has a fixed point in clU. Let C b
A harmonic map between two Riemannian manifolds is defined to be a critical point of the energy functional; the energy of a smooth map is by definition the integration of the squared norm of its differential over the source manifold. By solving the heat equation associated with t
As a continuation of previous work of the first author with S. Ranjbar [26] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear
The geometric median as well as the Fréchet mean of points in a Hadamard space are important in both theory and applications. Surprisingly, no algorithms for their computation are hitherto known. To address this issue, we use a splitting version of the proximal point algorithm fo