Construction of sunny nonexpansive retractions in Banach spaces

By T. Benavides, G. Acedo, Hong-Kun Xu. Bulletin of the Australian Mathematical Society, 2002

54 citations recorded by the source corpus.

Let  be a commutative family of nonexpansive self-mappings of a closed convex subset C of a uniformly smooth Banach space X such that the set of common fixed points is nonempty. It is shown that if a certain regularity condition is satisfied, then the sunny nonexpansive retraction from C to F can be constructed in an iterative way.

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

View Paper: https://www.semanticscholar.org/paper/074480aee012a2cab6a59eb5555c8756e41af2a1

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. Yonghong Yao
2. Yair Censor
3. Muhammad Aslam Noor
4. Arkady Aleyner
5. Yisheng Song
6. Sumei Xu
7. Khalida Inayat Noor
8. Dang Van Hieu

In Geometry and Topology

1. Yonghong Yao
2. Muhammad Aslam Noor
3. Arkady Aleyner
4. Yisheng Song
5. Yair Censor
6. Sumei Xu
7. Yeong-Cheng Liou

In Numerical Analysis

1. Yonghong Yao
2. Yair Censor
3. Muhammad Aslam Noor
4. Arkady Aleyner
5. Yisheng Song
6. Sumei Xu
7. Dang Van Hieu
8. Aviv Gibali

Citations in the corpus

• Strong convergence theorems for nonexpansive semigroup in Banach spaces (2008, background): “At the same time, the main conclusions of Dominguez Benavides, López Acedo and Xu [3], Aleyner and Censor [1, Theorem 20], Aleyner and Reich [2, Theorem 3.”
• BEST APPROXIMATION TO COMMON FIXED POINTS OF A SEMIGROUP OF NONEXPANSIVE OPERATORS (2005, background): “1 in the paper by Dominguez Benavides, Lopez Acedo and Xu [15] is not true.”
• On viscosity iterative methods for variational inequalities (2007, methodology): “For the convergence analysis of Algorithm 2, see [11].”