Related papers: A Generalization of Halpern Iteration. Preliminary…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper…
In this paper, we unify all know iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically $I$-nonexpansive mappings. Note that such a scheme…
In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive…
In this paper, we study, in a nonlinear setting, the asymptotic behaviour of a generalized viscosity approximation method associated with a countable family of nonexpansive mappings satisfying resolvent-like conditions. We apply proof…
The Irreversible Port-Hamiltonian Systems (IPHS) framework is extended to the modelling of non-isentropic fluids with viscous dissipation in the Eulerian description. Building on earlier IPHS formulations for diffusion-driven and…
In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points…
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 prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points. These are characteristic points for the level sets of the…
We give a rate of metastability for Halpern's iteration relative to a rate of metastability for the resolvent for nonexpansive mappings in uniformly smooth Banach spaces, extracted from a proof due to Xu. In Hilbert space, the latter is…
We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged…
A version of the globally convergent convexification numerical method is constructed for the problem of Electrical Impedance Tomography in the 2D case. An important element of this version is the presence of the viscosity term. Global…
Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron's method. If the equation is…
The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the hybrid steepest descent method is convergent whenever so is every iterative sequence generated by the Halpern type iterative…
We analyze the oracle complexity of the stochastic Halpern iteration with minibatch, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional space. We show that if the underlying…
In his recent research M. K. Tam (2018) considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. At each point in the ambient space, the value of the operator can…
In this paper we apply proof mining techniques to compute, in the setting of CAT$(\kappa)$ spaces (with $\kappa >0$), effective and highly uniform rates of asymptotic regularity and metastability for a nonlinear generalization of the…