Variational inequality problems over split fixed point sets of strict pseudo-nonspreading mappings and quasi-nonexpansive mappings with applications

Fixexd point theory and applications

Zenn-Tsun Yu¹  Lai-Jiu Lin² 

[1] Department of Electronic Engineering, Nan Kai University of Technology, Nantou, Taiwan;Department of Mathematics, National Changhua University of Education, Changhua, Taiwan

关键词: hierarchical problems;    split feasibility problem;    fixed point problem;    strict pseudo-nonspreading mappings;    pseudo-contractive mappings;   

DOI  :  10.1186/1687-1812-2014-198

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we first establish a strong convergence theorem for a variational inequality problem over split fixed point sets of a finite family of strict pseudo-nonspreading mappings and a countable family of quasi-nonexpansive mappings. As applications, we establish a strong convergence theorem of split fixed point sets of a finite family of strict pseudo-nonspreading mappings and a countable family of strict pseudo-nonspreading mappings without semicompact assumption on the strict pseudo-nonspreading mappings. We also study the variational inequality problems over split common solutions of fixed points for a finite family of strict pseudo-nonspreading mappings, fixed points of a countable family of pseudo-contractive mappings (or strict pseudo-nonspreading mappings) and solutions of a countable family of nonlinear operators. We study fixed points of a countable family of pseudo-contractive mappings with hemicontinuity assumption, neither Lipschitz continuity nor closedness assumption is needed.

【 授权许可】

CC BY