Viscosity explicit midpoint methods for nonexpansive mappings in Hadamard spaces

Abstract

In this paper, the viscosity explicit midpoint method for nonexpansive mappings in Hadamard spaces is introduced. Under certain appropriate conditions on the sequence of parameters, it is proved that the limit of the approximating sequence generated by proposed method converges strongly to a fixed point of T which solves some variational inequality. Moreover, we give an application to the equilibrium problem.