The general iterative scheme for semigroups of nonexpansive mappings and variational inequalities with applications

In this paper, we introduce the implicit and explicit viscosity iteration schemes for nonexpansive semigroups $\{T\left(t\right):t\ge 0\}$ . Additionally, it proves that the proposed iterative schemes converge strongly to a unique common fixed point of $\{T\left(t\right):t\ge 0\}$ in the framework of reflexive and strictly convex Banach space, which solves some variational inequality. The main results of this paper improve and generalize recent known results in the current literature.