Now showing items 1-10 of 16
Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces [Article]
(Springer Open, 2010)
We give a sufficient and necessary condition concerning a Browder’s convergence type theorem for uniformly asymptotically regular one-parameter nonexpansive semigroups in Hilbert spaces.
Proximal point algorithms on Hadamard manifolds: linear convergence and finite termination [Article]
(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 ...
The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem [Article]
(Society for Industrial and Applied Mathematics, 2018)
This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 ...
Equilibrium problems on Riemannian manifolds with applications [Article]
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 ...
What do 'convexities' imply on Hadamard manifolds? [Article]
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 ...
Monotone and accretive vector fields on Riemannian manifolds [Article]
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 ...
Rate of convergence under weak contractiveness conditions [Article]
(Casa Cartii de Stiinta, 2013)
We introduce a new class of selfmaps T of metric spaces, which generalizes the weakly Zamfirescu maps (and therefore weakly contraction maps, weakly Kannan maps, weakly Chatterjea maps and quasi-contraction maps with ...
Firmly nonexpansive mappings in classes of geodesic spaces [Article]
(American Mathematical Society, 2014)
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and ...
A fixed point theorem for weakly Zamfirescu mappings [Article]
In  T. Zamfirescu, Fixed point theorems in metric spaces, Arch. Math. 23 (1972), 292–298. Zamfirescu gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan and Chatterjea. In ...