Extension and Application of the Yamada Iteration Algorithm in Hilbert Spaces

Abstract

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 convergence theorems which are used to solve the equilibrium problem and the split feasibility problem.

Keywords

• Yamada iteration
• nonexpansive mappings
• inverse strongly-monotone mappings
• variational inequality
• zero point
• iterative method
• fixed point