A hybrid iterative method for common solutions of variational inequality problems and fixed point problems for single-valued and multi-valued mappings with applications

作者：Onjai uea Nawitcha; Phuengrattana Withun^*

来源：Fixed Point Theory and Applications, 2015, 2015(1): 16.

DOI：10.1186/s13663-015-0265-x

• fixed point
• strictly pseudononspreading mappings
• multi-valued mappings
• variational inequality problems
• Hilbert spaces

In this article, we propose a new iterative method for approximating a common element of the set of common fixed points of a finite family of k-strictly pseudononspreading single-valued mappings, the set of common fixed points of a finite family of quasi-nonexpansive multi-valued mappings, and the set of common solutions of a finite family of variational inequality problems in Hilbert spaces. Furthermore, we prove that the proposed iterative method converges strongly to a common element of the above three sets, and we also apply our results to complementarity problems. Finally, we give two numerical examples to support our main result.

• 出版日期2015-2-1