Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces

In this paper, the implicit midpoint rule of asymptotically nonexpansive mapping in CAT(0) spaces is introduced. By the viscosity approximation method, we prove that the proposed implicit iteration converges strongly to a fixed point of asymptotically nonexpansive mapping under certain assumptions imposed on the sequence of parameters. The results presented in the paper improve and extend various results in the existing literature.