1. Variational Inequality Problem Over the Set of Common Fixed Points of a Family of Demi-Contractive Mappings
- Author
-
Mohammad Eslamian
- Subjects
variational inequality problem ,demi-contractive mappings ,fixed point ,strict pseudo-contractive mappings. ,Mathematics ,QA1-939 - Abstract
In this paper, by using the viscosity iterative method and the hybrid steepest-descent method, we present a new algorithm for solving the variational inequality problem. The sequence generated by this algorithm is strong convergence to a common element of the set of common zero points of a finite family of inverse strongly monotone operators and the set of common fixed points of a finite family of demi-contractive mappings. Also, we prove that the sequence generated by this algorithm is strong convergence to a solution of a system of variational inequalities over the set of common fixed points of quasi-nonexpansive mappings and strict pseudo-contractive mappings in a Hilbert space. Finally, some applications of this results are present for solving the split common fixed point problem, which entails finding a point which belongs to the set of common fixed points of a finite family of of strict pseudo-contractive mappings in a Hilbert space such that its image under a linear transformation belongs to the set of common fixed points of a finite family of nonexpasive mappings in the image space../files/site1/files/63/1.pdf
- Published
- 2020