Contraction of the proximal mapping and applications to the equilibrium problem |
| |
Authors: | Ngoc Hai Trinh |
| |
Affiliation: | 1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam.hai.trinhngoc@hust.edu.vn |
| |
Abstract: | In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm. |
| |
Keywords: | Proximal mapping equilibrium problem variational inequality problem fixed-point problem contractive mapping nonexpansive mapping |
|
|