... CONVERGENCE THEOREMS FOR
NONEXPANSIVE SEMIGROUPS IN BANACH SPACES
SACHIKO ATSUSHIBA AND WATARU TAKAHASHI
Received 24 February 2005
We introduce an implicit iterative process for a nonexpansive ... Strong convergence theorems for finite quasi -nonexpansive mappings, Comm. Appl.
Nonlinear Anal. 9 (2002), no. 3, 57–68.
[2] , Strong convergence theorems...
... 2005.
5 W. Takahashi, Y. Takeuchi, and R. Kubota, Strong convergence theorems by hybrid methods for fam-
ilies of nonexpansive mappings in Hilbert spaces, ” Journal of Mathematical Analysis and Applications,
vol. ... He and R. Chen, Strong convergence theorems of the CQ method for nonexpansive semigroups, ”
Fixed Point Theory and Applications, vol. 2007, Artic...
... fixed points
of a nonexpansive mapping on a real Hilbert space H:
min
x∈C
1
2
Ax, x−x, b,
(1:7)
where C is the fixed point set of a nonexpansive mapping T on H and b is a given
point in H. In ... and Preechasilp: The modified general iterative methods for nonexpansive
semigroups in banach spaces
†
. Fixed Point Theory and Applications 2011 2011:76.
Wangkeeree an...
... Tianjin Natural Science Foundation in China Grant no.
06YFJMJC12500.
2 Fixed Point Theory and Applications
for fixed points of nonexpansive mapping T in Banach space and also prove weak and strong
convergence ... study weak and strong convergence theorems for common fixed points of a
finite family of nonexpansive mappings {T
i
}
N
i1
in Banach spaces....
... iteration and the modified Ishikawa iteration, Zhou 3
obtained some weak and strong convergence theorems for λ-strict pseudocontractions in
Hilbert spaces which extend the corresponding results in ... following four aspects: 1 in contrast to weak convergence results in 2–4 ,strong
convergence theorems of the modified Mann iterative sequence are obtained i...
... Genel and J. Lindenstrauss, “An example concerning fixed points,” Israel Journal of Mathematics,
vol. 22, no. 1, pp. 81–86, 1975.
7 K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive ... Anthony To Ming Lau
We introduce a modified Ishikawa iterative process for approximating a fixed point of two
in nitely nonexpansive self-mappings by using the hybrid m...
... 3andT
1
T
2
T
3
T in Theorem 3.4, we obtain strong convergence
theorem for Noor iteration scheme with error for asymptotically nonexpansive mapping T in
the intermediate sense in Banach ... establish strong convergence theorem for multi-step iterative scheme with errors for
asymptotically nonexpansive mappings in the intermediate sense in Banach spac...
... Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, ” Journal of
Mathematical Analysis and Applications, vol. 67, no. 2, pp. 274–276, 1979.
[5] T H. Kim and H K. Xu, Strong ... certain control conditions for modified
Mann iteration,” to appear in Nonlinear Analysis: Theory, Methods & Applications .
[7] W. Takahashi and K. Shimoji, Converg...
... Shioji and W. Takahashi, Strong convergence theorems for asymptotically nonexpansive
semigroups in Hilbert spaces, ” Nonlinear Analysis, vol. 34, no. 1, pp. 87–99, 1998.
[3] T. Suzuki, “On strong convergence ... 8
pages, 2007.
[9] K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and
nonexpansive semigroups, ” Journal of Ma...
... easily obtain hybrid methods introduced by Nakajo and Takahashi
3 for a nonexpansive mapping.
Recently, Takahashi et al. 4 proposed a shrinking projection method for nonexpan-
sive mappings T
n
: ... H.
Inspired by Bauschke and Combettes 1 and Takahashi et al. 4, we present a
shrinking projection method for the class of T mappings. Furthermore, we obtain a shrinkin...