Abstract
The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 2260-2270 |
| Number of pages | 11 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 73 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 1 Oct 2010 |
Keywords
- α-inverse- strongly monotone mapping
- Equilibrium problem
- Generalized equilibrium problem
- Maximal monotone operator
- Relatively nonexpansive mapping
- Variational inequality
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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