Abstract
The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F(S) of fixed points of a relatively nonexpansive mapping S, and the set T -1 0 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems for these hybrid proximal-type algorithms are established; that is, under appropriate conditions, the sequences generated by these various algorithms converge strongly to the same point in EPF(S) T -1 0. These new results represent the improvement, generalization, and development of the previously known ones in the literature.
| Original language | English |
|---|---|
| Article number | 973028 |
| Journal | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Volume | 2011 |
| DOIs | |
| State | Published - 2011 |
Bibliographical note
Funding Information:This research was partially supported by the Leading Academic Discipline Project of Shanghai Normal University (no. DZL707), Innovation Program of Shanghai Municipal Education Commission Grant (no. 09ZZ133), National Science Foundation of China (no. 11071169), Ph.D. Program Foundation of Ministry of Education of China (no. 20070270004), Science and Technology Commission of Shanghai Municipality Grant (no. 075105118), and Shanghai Leading Academic Discipline Project (no. S30405). Al-Homidan is grateful to KFUPM for providing research facilities.
ASJC Scopus subject areas
- Geometry and Topology
- Applied Mathematics
Fingerprint
Dive into the research topics of 'Hybrid proximal-type algorithms for generalized equilibrium problems, maximal monotone operators, and relatively nonexpansive mappings'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver