A Geometrical Look at Iterative Methods for Operators with Fixed Points

By Gilbert Crombez. 2005

56 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/df9de36699130884c3dfb3673215e863e622e8b1

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

1. Aviv Gibali
2. Simeon Reich
3. Yair Censor
4. S. H. Rizvi
5. Kaleem Raza Kazmi
6. Charles L. Byrne
7. Dang Van Hieu
8. Yazheng Dang

In Geometry and Topology

1. Yazheng Dang
2. Yan Gao
3. S. H. Rizvi
4. Kaleem Raza Kazmi
5. Aviv Gibali
6. Simeon Reich
7. Yair Censor
8. Charles L. Byrne

In Numerical Analysis

1. Aviv Gibali
2. Simeon Reich
3. Yair Censor
4. S. H. Rizvi
5. Kaleem Raza Kazmi
6. Dang Van Hieu
7. Yazheng Dang
8. Yan Gao

Citations in the corpus

• A Hierarchical Presentation of Operators with Fixed Points on Hilbert Spaces (2006, methodology): “The implications (i) ⇒ (ii) ⇒ (iii) ⇒ (v) ⇒ (i) have been shown in [12] [Theorem 2.”
• Algorithms for the Split Variational Inequality Problem (2010, background): “This class coincides with the class F for = 1 [25] and with the class DCp for p = 1 [32].”
• An iterative method for solving split monotone variational inclusion and fixed point problems (2015, unknown): “1 [13,14] Let H be a Hilbert space and T : H → H a nonexpansive mapping, then for all x, y ∈ H, 〈(x − T x) − (y − T y), T y − T x〉 ≤ 1 2 ||(T x − x) − (T y − y)||2 (2.”
• Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup (2013, background): “, Theorem 3 in [14] and Theorem 1 in [15]).”
• Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem (2011, unknown): “Indeed, by the above equalities we get ( JB1λ ( I − γA∗(I − JF1λ )A )) (z) = JB1λ (z − γA∗(I − JF1λ )Az) = JB1λ (z) = z. (3.8) Since Γ 6= ∅, we get from [11, Proposition 2.2] (see also [7, Lemma 2.1]), with the averaged operators I − γA∗(I − JF1λ )A and JB1λ , that Fix(JB1λ ) ∩ Fix(I − γA∗(I − JF1λ…”
• The strong convergence of a KM–CQ-like algorithm for a split feasibility problem (2010, methodology): “The Krasnosel’skii–Mann (KM) algorithm was proposed initially for solving the fixed point problem T x = x, where T is a self-mapping of a closed convex set, see [5].”
• The Split Common Null Point Problem (2011, background): “This class coincides with the class F for ν = 1 [31] and with the class DCp”