Extension and Application of the Yamada Iteration Algorithm in Hilbert Spaces

Ming Tian, Meng-Ying Tong
2019 Mathematics  
In this paper, based on the Yamada iteration, we propose an iteration algorithm to find a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping. We obtain a weak convergence theorem in Hilbert space. In particular, the set of zero points of an inverse strongly-monotone mapping can be transformed into the solution set of the variational inequality problem. Further, based on this result, we also obtain some new weak
more » ... ome new weak convergence theorems which are used to solve the equilibrium problem and the split feasibility problem.
doi:10.3390/math7030215 fatcat:wd7otw6i6rb2rasctl6r4pgima