Subsequently, Nadezhkina and Takahashi in [16] applied the method for finding a common element of the set of fixed points of a

nonexpansive mapping and the set of solutions of variational inequality.

2) and a

nonexpansive mapping by an iterative method.

Let X be a uniformly convex Banach space and let Q be a

nonexpansive mapping of X into X (i.

Let F be a bi- function from C x C to R satisfying (A1) - (A4) and let S be a

nonexpansive mapping of C into H such that F(S) [intersection] EP(f) [not equal to] 0.

A

nonexpansive mapping T on X with F(T) [not equal to] [empty set] is quasi-nonexpansive, but not conversely (see [20], p.

Nadezhkina and Takahashi [17] introduced a so-called extragradient method motivated by the idea of Korpelevich [8] for finding a common element of the set of fixed points of a

nonexpansive mapping and the set of solutions of a variational inequality problem and obtained a weak convergence theorem.

For instance, the fixed point of the

nonexpansive mapping T: [0,1] [right arrow] [0,1] defined by

Lau, Amenability and fixed point property for semigroup of

nonexpansive mappings, in : M.

His text is organized in eight sections and covers geometry of nonpositive curvature, convex sets and convex functions, weak convergence in Hadamard spaces,

nonexpansive mappings, gradient flow of a convex functional, convex optimization algorithms, probablitistic tools in Hadamard spaces, and Tree Space and its applications.

The study of fixed points for multivalued contractions and

nonexpansive mappings using the Hausdorff metric was initiated by Markin [1].

Prempeh: Strong convergence theorems for a finite family of

nonexpansive mappings in Banach spaces, Comm.

Chang, Some results for asymptotically pseudocontractive mappings and asymptotically

nonexpansive mappings, Proc.