Fixed point theorems and convergence theorems for a generalized nonexpansive mapping in uniformly convex Banach spaces

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]