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

Abstract

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

• Strong convergence
• Iterative scheme
• Split monotone variational inclusion
• Variational inequality
• Fixed point
• k-strict pseudo-contractions