... fixed point theorems
in symmetric spaces for weakly compatible maps. The main purpose of this paper
is to give some common fixed point theorems for weakly compatible selfmappings of
o -metric spaces.
We ... observed in [3] that some of the defining properties of the metric
are not needed in the proofs of certain metric theorems. Motivated by this fact, Hicks
in...
... pages
doi:10.1155/2011/216173
Research Article
Convergence of Iterative Sequences for Common
Zero Points of a Family of m-Accretive Mappings in
Banach Spaces
Yuan Qing,
1
Sun Young Cho,
2
and Xiaolong Qin
1
1
Department of ... αα
n
}.Inviewof
Lemma 2.4, we can obtain the desired conclusion easily. This completes the proof.
As an application of Theorems 3.1 and 3.2, we have...
... nonexpansive mappings, ”
Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972.
2 J. Schu, “Iterative construction of fixed points of asymptotically nonexpansive mappings, ” Journal ... subset of a reflexive Banach space E with a weakly continuous
dual mapping, and let {T
i
}
∞
i1
be an in nite countable family of asymptotically nonexpansive
mappings wit...
... convergence t 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 ... duality mapping from E into E
∗
. Then J
−1
is also single-valued, one-to-one, and surjective,
and it is the duality mapping from E
∗
into E. We make use of the following mapping...
... pages
doi:10.1155/2009/804734
Research Article
Some Common Fixed Point Theorems for Weakly
Compatible Mappings in Metric Spaces
M. A. Ahmed
Department of Mathematics, Faculty of Science, Assiut University, ... fixed point theorem for weakly compatible mappings generalizing a result
of Khan and Kubiaczyk 1988. Also, an example is given to support our generalization. We a...
... point of a finite family of nonexpansive mappings in Banach spaces. Let C
beanonemptyclosedconvexsubsetofaBanachspaceE and let
{T
i
}
m
i
=1
be a finite family
of nonexpansive mappings from C into ... problem of image recovery in the
setting of Hilbert spaces is a common fixed point problem for a family of nonexpansive
mappings.
A well-known method for finding a solution...
... 2.12.
In the following example, we give a broad class of ws-compact mappings which are
not sequentially weakly continuous.
2 Fixed Point Theory and Applications
all nonempty bounded subsets of X ... continue the study of ws-compact mappings, investigate the boundary conditions,
and establish new fixed point theorems. Specifically, we prove several fixed point theorems
for ws-compact...
... approximation of fixed points of compositions of nonexpansive mappings in
Hilbert space, J. Math. Anal. Appl. 202 (1996), no. 1, 150–159.
[2] F.E.Browder,Convergence of approximants to fixed points of nonexpansive ... points of nonexpansive mappings in Banach
spaces, J.Math.Anal.Appl.302 (2005), no. 2, 509–520.
[9] J.S.JungandT.H.Kim,Convergence of approximate sequences f...
... sequences of real numbers defined for n ∈ N
{0, 1, 2, } and 0 <a
l
≤ a
u
,0<b
l
≤ b
u
. Similarly to the proof of Propositions 1 and 3 in 12,
we can obtain the following.
Hindawi Publishing ... 4 Advances in Difference Equations
2. Proof of Theorem 1.2
The following lemma can be found in 10.
Lemma 2.1. Assume that A>0 and y0 > 0, ... d
u
i
H
i
M
i
⎫
⎬
⎭
.
2.23...
... r
f ∈ ε(n) ω
Diff
r
(n)
1. Introduction
“ f
0 0
f 0 ”
[5]
[2]
f ∈ ε(n) ω Diff (n)
ω
K|
x
1
|
x
1
K
0 {x
1
= 0}
f ∈ ε(n) ω Diff
r
(n)
ω
f ∈ ε(n) ω Diff
r
(n)
2. Preliminaries
ε(n, p) R
n
R
p
ε(n) ... Preliminaries
ε(n, p) R
n
R
p
ε(n) ε(n, 1) r ∈ N, 0 ≤ r ≤ n I = {1, , r}
1
- Rec eived 30/09/2005, in revised form 20/01/2006.
X
i
{(x
1
, x
2
, , x
n
) ∈ R
n
: x
i
= 0} i ∈ I P (I)
I
X = {X...