A general iterative method for nonexpansive mappings in Hilbert spaces

By Giuseppe Marino, Hong-Kun Xu. 2006

598 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/60853863fc63a12859af0013018f249b6fc0eae7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup (2013, methodology): “[1] Assume that B is a strong positive linear bounded operator on a Hilbert space H1 with coefficient γ̄ > 0 and 0 < ρ < ‖B‖−1.”
A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces (2008, methodology): “Recently, Marino and Xu [8] introduced a new iterative scheme by the viscosity approximation method [9]: xn+1 = ( I −αnA ) Sxn +αnγ f ( xn ) , n≥ 0.”
New Methods with Perturbations for Non-Expansive Mappings in Hilbert Spaces (2011, background): “Recently, iterative methods for finding fixed points of non-expansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [1-34] and the references th”
Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings (2007, methodology): “Recently, Marino and Xu [1] introduced a new iterative scheme by the viscosity approximation method xn+1 = ( I −αnA ) Sxn +αnγ f ( xn ) , n≥ 0.”
Towards viscosity approximations of hierarchical fixed-point problems (2006, background): “1) reduces to the problem of minimizing a quadratic function over the set of fixed points of a nonexpansive mapping studied in Marino and Xu [5], namely, 〈 (A− γ f )x,x− x〉≥ 0, ∀x ∈ FixP, (2.”