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 · Journal of Inequalities and Applications · 2018
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.