Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings

By Yongfu Su, Dongxing Wang, Meijuan Shang. 2007

78 citations recorded by the source corpus.

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others.

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

View Paper: https://www.semanticscholar.org/paper/4d26f9f057dd3cb59b3c097c3c2c76b0840a8023

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In Computational Theory and Mathematics

1. Kriengsak Wattanawitoon
2. Narin Petrot
3. Bing Tan
4. Poom Kumam
5. Haiyun Zhou
6. G. Gao
7. Jong Kyu Kim

In Geometry and Topology

1. Bing Tan
2. Poom Kumam
3. Kriengsak Wattanawitoon
4. Narin Petrot
5. Haiyun Zhou
6. G. Gao
7. Jong Kyu Kim
8. Wutiphol Sintunavarat

In Numerical Analysis

1. Narin Petrot
2. Kriengsak Wattanawitoon
3. Bing Tan
4. Poom Kumam
5. Haiyun Zhou
6. G. Gao
7. Jong Kyu Kim

Citations in the corpus

• Convergence theorems of a modified hybrid algorithm for a family of quasi-φ-asymptotically nonexpansive mappings (2010, result): “The results of this paper improve and extend the results of Nakajo and Takahashi [6], Kim and Xu [4], Carlos and Xu [8], Matsushita and Takahashi [9], Su and Qin [15], Su, Wang and Shang [ 16 ], He and Chen [17] and others.”
• A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces (2010, background): “A mapping T from C into itself is said to be relatively nonexpansive [33–35] if F̂(T ) = F(T ) and φ(p, Tx) ≤ φ(p, x) for all x ∈ C and p ∈ F(T ).”