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Artículo
Iterative algorithms for nonexpansive mappings on Hadamard manifolds
(The Mathematical Society of the Republic of China, 2010-04)
Two iterative algorithms for nonexpansive mappings on Hadamard manifolds, which are extensions of the well-known Halpern's and Mann's algorithms in Euclidean spaces, are proposed and proved to be convergent to a fixed ...
Artículo
Best simultaneous approximation to totally bounded sequences in Banach spaces
(Springer, 2008-09)
This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the ...
Artículo
Equilibrium problems on Riemannian manifolds with applications
(Elsevier, 2019-05-15)
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium ...
Artículo
Proximal point algorithms on Hadamard manifolds: linear convergence and finite termination
(Society for Industrial and Applied Mathematics, 2016)
In the present paper, we consider inexact proximal point algorithms for finding singular points of multivalued vector fields on Hadamard manifolds. The rate of convergence is shown to be linear under the mild assumption ...
Artículo
Monotone and accretive vector fields on Riemannian manifolds
(Springer, 2010-09)
The relationship between monotonicity and accretivity on Riemannian manifolds is studied in this paper and both concepts are proved to be equivalent in Hadamard manifolds. As a consequence an iterative method is obtained ...
Artículo
Stable and total Fenchel duality for convex optimization problems in locally convex spaces
(Society for Industrial and Applied Mathematics, 2009)
We consider the optimization problem (PA) infx∈X{f(x) + g(Ax)} where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y, respectively, and A is a linear operator from ...
Artículo
What do 'convexities' imply on Hadamard manifolds?
(Springer, 2016-09)
Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these ...