  In this paper, we prove the existence of fixed points of mappings satisfying
the condition (Da), a kind of generalized nonexpansive mappings, on a weakly
compact convex subset in a Banach space satisfying Opial's condition. And we
use Sahu([6]) and Thakur([10])'s iterative scheme to establish several
convergence theorems in uniformly convex Banach spaces and give an example to
show that this scheme converges faster than the scheme in [1]
