Split equality monotone variational inclusions and fixed point problem of set-valued operator

Abstract

In this paper, we are concerned with the split equality problem of finding an element in the zero point set of the sum of two monotone operators and in the common fixed point set of a finite family of quasi-nonexpansive set-valued mappings. Strong convergence theorems are established under suitable condition in an infinite dimensional Hilbert spaces. Some applications of the main results are also provided.

Keywords

• split equality problem
• monotone variational inclusions
• quasi-nonexpansive
• set-valued mappings
• 47j25
• 47n10
• 65j15
• 90c25