Báo cáo hóa học: " Research Article Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces" docx
... heorems for finding a common fixed point of
a finite family of relatively nonexpansive mappings in Banach spaces by using the hybrid
method in mathematical programming.
Theorem 3.1. Let E be a uniformly ... Feasibility
Problems and Fixed Point Problems of Relatively
Nonexpansive Mappings in Banach Spaces
Somyot Plubtieng and Kasamsuk Ungchittrakool...
... system of variational inclusions/inequalities arise in applications to variational problems
and engineering, see; for example, 1–31. Variational inclusions/inequalities can be viewed
as innovative ... innovative and novel extension of the variational principles.
Inspired and motivated by research going on in this area, we introduce and consider
a new system of extend...
... r
n1
|
,
3.18
Journal of Inequalities and Applications 5
the set of fixed points of a nonexpansive mapping, the set of solutions of the variational
inequalities for a relaxed cocoercive mapping, and the set of solutions ... α
n
Ty
n
,
1.8
for approximating a common element of the set of fixed points of a nonexpansive nonself
mapping and the set of soluti...
... family of relatively nonexpansive mappings in a Banach
space. We first prove that the fixed -point set of this operator is identical to the set of all
common fixed points of the mappings. Next, using ... family of nonexpansive mappings in Banach spaces. Let C
beanonemptyclosedconvexsubsetofaBanachspaceE and let
{T
i
}
m
i
=1
be a finite family
of nonexpansive...
... defining convergent and Cauchy sequences in the terms of interior points of
the underlying cone. These and other authors see, e.g., 8–22 proved some fixed point and
common fixed point theorems for ... ·
d
fx,gx
d
fy,gy
, 3.25
Fixed Point T heory and Applications 5
Recall that a point u ∈ X is called a coincidence point of the pair f, g and v i...
... 2008.
18 S. Plubtieng and R. Punpaeng, “A new iterative method for equilibrium problems and fixed
point problems of nonexpansive mappings and monotone mappings, ” Applied Mathematics and
Computation, ... Kumam and P. Katchang, “A viscosity of extragradient approximation method for finding equi-
librium problems, variational inequalities and fixed point prob...
... equilibrium problems and fixed
point problems of nonexpansive mappings and monotone mappings, ” Applied Mathematics and
Computation, vol. 197, no. 2, pp. 548–558, 2008.
12 X. Qin, M. Shang, and Y. ... 199–215,
2010.
9 P. Kumam, “A hybrid approximation method for equilibrium and fixed point problems for a
monotone mapping and a nonexpansive mapping,” Nonl...
... mapping T if x ∈ Tx.
We use the notation FixT standing for the set of fixed points of a mapping T and
Fixt ∩ FixT standing for the set of common fixed points of t
and T. Precisely, a point ... compact convex subset of a uniformly convex Banach space X ,and
let t : E → E and T : E → FBE be a single-valued and a multivalued nonexpansive mapping,
6 Fixed...
... C. Liou, and J C. Yao, “Convergence theorem for equilibrium problems and fixed point
problems of in nite family of nonexpansive mappings, ” Fixed Point Theory and Applications, vol. 2007,
Article ... element of
the set of solutions of generalized equilibrium problems, the set of common fixed
points of in nitely many nonexpansive mappings, and the set...
... mapping. They also introduced and studied a new class of nonlinear varia-
tional inclusions involving maximal η-monotone mapping in Hilbert spaces.
Motivated and inspired by the research work going ... going on in this field, we introduce and
study a new class of generalized nonlinear set-valued quasivariational inclusions involv-
ing generalized m-accretive mappings in Ba...