A new modified semi-implicit midpoint rule for nonexpansive mappings and 2-generalized hybrid mappings

In this paper, we present a new modified semi-implicit midpoint rule with the viscosity technique for finding a common fixed point of nonexpansive mappings and 2-generalized hybrid mappings in a real Hilbert space. The proposed algorithm is based on implicit midpoint rule and viscosity approximation method. Under some mild conditions, the strong convergence of the iteration sequences generated by the proposed algorithm is derived.