Related papers: Viscosity iteration in CAT(k) spaces

In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in…

We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…

We propose a Deep-Picard iteration framework for high-dimensional nonlinear space-time fractional diffusion equations.The method is based on a nonlinear fractional Feynman--Kac fixed-point formulation, which replaces direct discretization…

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

We use $KKM$ theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and $A:M\rightarrow M$ be a non-expansive mapping, then exists a fixed point of A…

In the setting of hyperbolic spaces, we show that the convergence of Browder-type sequences and Halpern iterations respectively entail the convergence of their viscosity version with a Rakotch map. We also show that the convergence of a…

We prove weak and strong convergence theorems for a double Krasnoselskij type iterative method to approximate coupled solutions of a bivariate nonexpansive operator F : C x C --> C, where C is a nonempty closed and convex subset of a…

Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental…

A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the…

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a…

In this paper, we discuss the fixed point property for an infinite family of order-preserving mappings which satisfy the Lipschitzian condition on comparable pairs. The underlying framework of our main results is a metric space of any…

In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…

In this note, at first we prove that the existence of best proximity points for cyclic relatively nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic relatively nonexpansive mappings in the setting of…

This paper focuses on designing a consistent and efficient filter for map-based visual-inertial localization. First, we propose a new Lie group with its algebra, based on which a novel invariant extended Kalman filter (invariant EKF) is…

We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show…

This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…

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…

In this paper, we show that, under appropriate conditions, there exists a quasinonexpansive extension of a mapping with an attractive point in the sense of Takahashi and Takeuchi (2011) such that the fixed point set of the extension equals…

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\{T_j\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of…