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Ponencia
Applications of convex analysis within mathematics
(2016)
This talk is based on the paper: Aragón, Borwein, Martín-Márquez, Yao Applications of convex analysis within mathematics, Math. Program., Ser B, December 2014, Volume 148, Issue 1, pp 49-88. in a special issue to celebrate ...
Artículo
Iterative methods for approximating fixed points of Bregman nonexpansive operators
(American Institute of Mathematical Sciences, 2013-08)
Diverse notions of nonexpansive type operators have been extended to the more general framework of Bregman distances in reflexive Banach spaces. We study these classes of operators, mainly with respect to the existence ...
Artículo
Applications of convex analysis within mathematics
(Springer, 2014-12)
In this paper, we study convex analysis and its theoretical applications. We apply important tools of convex analysis to Optimization and to Analysis. Then we show various deep applications of convex analysis and especially ...
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 ...
Capítulo de Libro
Existence and approximation of fixed points of right Bregman nonexpansive operators
(Springer, 2013-07-29)
We study the existence and approximation of fixed points of right Bregman nonexpansive operators in reflexive Banach space. We present, in particular, necessary and sufficient conditions for the existence of fixed points ...
Artículo
Right Bregman nonexpansive operators in Banach spaces
(Elsevier, 2012-09)
We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces. These classes of operators are associated with the Bregman distance induced by a convex function. In particular, we characterize ...
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
Nonexpansive mappings and monotone vector fields in Hadamard manifolds
(Dynamic Publishers, 2009)
This paper briefly surveys some recent advances in the investigation of nonexpansive mappings and monotone vector fields, focusing in the extension of basic results of the classical nonlinear functional analysis from Banach ...
Artículo
Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular
(Springer, 2012)
Because of Minty’s classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of basic importance in fixed point theory, ...