Variational inequality problems over split fixed point sets of strict pseudo-nonspreading mappings and quasi-nonexpansive mappings with applications
Zenn-Tsun Yu, Lai-Jiu Lin · Fixed Point Theory and Applications · 2014
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.