相关论文: Rates of asymptotic regularity for Halpern iterati…

In this paper we generalize the strongly convergent Krasnoselskii- Mann-type iteration for families of nonexpansive mappings defined recently by Bo\c{t} and Meier in Hilbert spaces to the abstract setting of W - hyperbolic spaces and we…

We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive -- or which satisfy the more general property $(P_2)$ -- is asymptotically regular, conditional on its fixed point set…

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 the asymptotic…

Bauschke and Moursi have recently obtained results that implicitly contain the fact that the composition of finitely many averaged mappings on a Hilbert space that have approximate fixed points also has approximate fixed points and thus is…

In this paper, inspired by Iemoto and Takahashi [S. Iemoto, W. Takahashi, Nonlinear Analysis 71, (2009), 2082-2089], we study the Halpern's method to approximate strongly fixed points of a nonexpansive mapping and of a nonspreading mapping.…

We investigate the asymptotic behavior of Halpern-type iterations applied to quasi-nonexpansive operators arising in best approximation problems over the intersection of finitely many closed convex sets in $\mathbb{R}^n$. Assuming a local…

We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…

We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of…

This paper investigates optimal error bounds and convergence rates for general Mann iterations for computing fixed-points of non-expansive maps. We look for iterations that achieve the smallest fixed-point residual after $n$ steps, by…

The Krasnosel'ski\u{\i}--Mann and Halpern iterations are classical schemes for approximating fixed points of nonexpansive mappings in Banach spaces, and have been widely studied in more general frameworks such as $CAT(\kappa)$ and, more…

Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

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, monotone operator…

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly…

This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction of this rate from an ineffective proof due to…

This paper investigates the minimax-optimality of Halpern fixed-point iterations for Lipschitz maps in general normed spaces. Starting from an a priori bound on the orbit of iterates, we derive non-asymptotic estimates for the fixed-point…

This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell^{1}$. We also point…

In this paper, we consider the Halpern iteration scheme for a finite family of quasinonexpansive mappings and then prove a strong convergence theorem to their common fixed point in a complete geodesic space with curvature bounded above by…

We apply proof mining methods to analyse a result of Boikanyo and Moro\c{s}anu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform…