Let H be a

uniformly convex Banach space and the set Q be a closed, bounded, and convex subset of H.

Let E be a

uniformly convex Banach space with a Frechet differentiable norm and let C be a nonempty subset of E.

[3] (Demiclosed principle) Let C be a nonempty closed convex subset of a

uniformly convex Banach space E and S : C [right arrow] C be a nonexpansive mapping.

As an example, any locally

uniformly convex Banach space (in particular, any

uniformly convex Banach space) possesses the Kadec-Klee property (see Diestel [8, Chapter 2, Theorem 3 and Theorem 4(iii)]).

Using these, we present some examples, one of which is a

uniformly convex Banach space which is not p-uniformly convex.

Let X be a

uniformly convex Banach space; for any bounded set B of X, there exist k, l > 0 and T > 0, and a finite dimension subspace [X.sub.1] of X, such that

Let E be a

uniformly convex Banach space, C be a nonempty closed convex subset of E, and S:C [right arrow] C be a nonexpansive mapping.

Let E be a

uniformly convex Banach space and 0 < p [less than or equal to] [t.sub.n] [less than or equal to] q < 1 for all n [member of] N.

If X is a

uniformly convex Banach space, then the inequality

It is known (cf.[4, 13]) that [W.sup.1,p](G, [[omega].sub.0], [[omega].sub.1]) is a

uniformly convex Banach space, provided

Recently, many authors studied a great number of iterative methods for solving a common element of the set of fixed points for a nonexpansive mapping and the set of solutions to a mixed equilibrium problem in the setting of Hilbert space and uniformly smooth and

uniformly convex Banach space, respectively (please see, e.g., [1-11] and the references therein).

Let E be a

uniformly convex Banach space, K be a nonempty closed convex subset of E.