2) and a nonexpansive mapping
by an iterative method.
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.
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
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
Other topics include Halpern's iteration for nonexpansive mappings
, Lie generators for local semigroups, generalized relaxations of nonexpansive operators, and split common fixed points.
n(mod N)], is called the implicit iteration process for a finite family of nonexpansive mappings
Reich: Uniform convexity, hyperbolic geometry, and nonexpansive mappings
Noor, Fixed point iterations for asymptotically nonexpansive mappings
in Banach spaces.
Toyoda: Approximation of common fixed points of a countable family of nonexpansive mappings
in a Banach space, Nonlinear Anal.
Narang: Common fixed points and invariant approximations for Cq-commuting generalized nonexpansive mappings
, Iranian J.