Using the concept of Bregman W-mapping, we propose a parallel hybrid extragradient algorithm for approximating a common element of the set of solutions of pseudomonotone equilibrium problems and split common fixed point problems of Bregman weak relatively nonexpansive mappings. With the algorithm, we state and prove a strong convergence result for finding a common solution of finite family of equilibrium problem and split common fixed point problem in a real Banach space. The stepsize for the split common fixed point problem is chosen in such a way that the algorithm does not require a prior estimation of the operator norm. Finally, we present an application of our results to variational inequality problems. Our result improves and extends some existing results in the literature in these directions.
|Number of pages||26|
|Journal||Bulletin of the Malaysian Mathematical Sciences Society|
|Publication status||Published - 1 Mar 2020|
- Bregman W-mapping
- Hybrid extragradient method
- Pseudomonotone equilibrium problem
- Split common fixed point problem