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

Fixexd point theory and applications

Nawitcha Onjai-uea¹  Withun Phuengrattana¹ 

[1] Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University, Nakhon Pathom, Thailand

关键词: fixed point;    strictly pseudononspreading mappings;    multi-valued mappings;    variational inequality problems;    Hilbert spaces;    46C05;    47H09;    47H10;   

DOI  :  10.1186/s13663-015-0265-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY