Strong convergence theorem for split monotone variational inclusion with constraints of variational inequalities and fixed point problems

Jin-Lin Guan; Lu-Chuan Ceng; Bing Hu

doi:10.1186/s13660-018-1905-6

Strong convergence theorem for split monotone variational inclusion with constraints of variational inequalities and fixed point problems

J Inequal Appl. 2018;2018(1):311. doi: 10.1186/s13660-018-1905-6. Epub 2018 Nov 15.

Authors

Jin-Lin Guan¹, Lu-Chuan Ceng¹, Bing Hu²

Affiliations

¹ 1Department of Mathematics, Shanghai Normal University, Shanghai, China.
² 2LAMPS and Department of Mathematics and Statistics, York University, Toronto, Canada.

Abstract

In this paper, inspired by Jitsupa et al. (J. Comput. Appl. Math. 318:293-306, 2017), we propose a general iterative scheme for finding a solution of a split monotone variational inclusion with the constraints of a variational inequality and a fixed point problem of a finite family of strict pseudo-contractions in real Hilbert spaces. Under very mild conditions, we prove a strong convergence theorem for this iterative scheme. Our result improves and extends the corresponding ones announced by some others in the earlier and recent literature.

Keywords: Fixed point; Hilbert spaces; Iterative scheme; Split monotone variational inclusion; Strong convergence; Variational inequality; k-strict pseudo-contractions.