On Fixed Points Theorem for α-β-Nonexpansive Mappings in Banach Spaces

In this paper,a new nonexpansive mapping is introduced in Banach space.It obtains that a necessary and sufficient condition for the nonexpansive mapping exists fixed points in uniformly convex Banach space.It shows that the Ishikawa iteration sequence is convergent to a fixed point of the nonexpansive mapping.Finally,it obtains that a necessary and sufficient condition for the sequence is of strong convergence to a fixed point of the nonexpansive mapping.