Subsequently, Nadezhkina and Takahashi in  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 , p.
Nadezhkina and Takahashi  introduced a so-called extragradient method motivated by the idea of Korpelevich  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 .
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