weak convergence and norm convergence implies strong convergence
Báo cáo toán học: " Weak and strong convergence theorems of implicit iteration process on Banach spaces" pdf
Ngày tải lên :
20/06/2014, 21:20
... Banach space and let E* b e the dual space of E. For a
sequence {x
n
}ofE and a point x ẻ E, the weak convergence of {x
n
}tox and the strong
convergence of {x
n
}tox are denoted by x
n
x and x
n
đ ... Lin et al.: Weak and strong convergence theorems of implicit iteration process on Banach
spaces. Fixed Point Theory and Applications 2011 2011:96.
Submit your manuscript to a
journal and benefi ... J: Weak and strong convergence to fixed points of asymptotically non-expansive mappings. Bull Austral Math
Soc. 43, 153–159 (1991). doi:10.1017/S0004972700028884
Lin et al. Fixed Point Theory and...
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Báo cáo toán học: " Weak and strong convergence theorems of implicit iteration process on Banach spaces" doc
Ngày tải lên :
20/06/2014, 21:20
... Banach space and let E* b e the dual space of E. For a
sequence {x
n
}ofE and a point x ẻ E, the weak convergence of {x
n
}tox and the strong
convergence of {x
n
}tox are denoted by x
n
x and x
n
đ ... Lin et al.: Weak and strong convergence theorems of implicit iteration process on Banach
spaces. Fixed Point Theory and Applications 2011 2011:96.
Submit your manuscript to a
journal and benefi ... two nonexpansive mappings and a relative nonexpansive mapping on Banach
spaces. Note that the conditions of strong convergence theorem are different from the
strong convergence theorems for the...
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Báo cáo hóa học: " Research Article Weak and Strong Convergence Theorems for Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense" pptx
Ngày tải lên :
21/06/2014, 11:20
... 3502–3511,
2009.
8 M. O. Osilike and S. C. Aniagbosor, Weak and strong convergence theorems for fixed points of
asymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 32, ... κ-strict pseudocontractions was introduced by Qihou 4 in 1996
see also 5.KimandXu6 studied weak and strong convergence theorems for this class
of mappings. It is important to note that every ... 2007.
11 G. Marino and H K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in
Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1,...
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Báo cáo toán học: " Strong convergence theorems and rate of convergence of multi-step iterative methods for continuous mappings on an arbitrary interval" pptx
Ngày tải lên :
20/06/2014, 20:20
... spaces, Fixed Point Theory and Appl., vol. 2010,
Article ID 262691, 12 (2010)
[20] Takahashi, W: Weak and strong convergence theorems for families of nonexpansive
mappings and their applications. ... appeared upon acceptance. Fully formatted
PDF and full text (HTML) versions will be made available soon.
Strong convergence theorems and rate of convergence of multi-step iterative
methods for ... problems and fixed point problems with applications. Nonlinear Anal.
72, 99–112 (2010)
[18] Shimoji, K, Takahashi, W: Strong convergence to common fixed points of infinite
nonexpansive mappings and applications....
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Báo cáo hóa học: " Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems" ppt
Ngày tải lên :
20/06/2014, 22:20
... al.: Strong convergence of a hybrid method for monotone variational inequalities and
fixed point problems. Fixed Point Theory and Applications 2011 2011:53.
Submit your manuscript to a
journal and ... {z
n
} converge weakly to
thesameelementof
N
i
=1
Fix(S
i
) ∩
if and only if lim inf
n
〈Ax
n
, x - x
n
0, x ẻ C.
Note that Ceng, Teboulle and Yao’s method has only weak convergence. Very ... approximation method are well defined and converge strongly
to P
F(S)∩Ω
.
Moti vated and inspired by the works of Nadezhkina and Takaha shi [23], Ceng et al.
[25], and Ceng et al. [27], in this paper...
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Báo cáo hóa học: " Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities" potx
Ngày tải lên :
20/06/2014, 22:20
... 1
n
0
T(t)y
n
dt, n ≥ 0
.
Then {x
n
} and {y
n
} convergence strongly to x* which is the unique solution of the sys-
tems of variational inequalities:
Piri and Badali Fixed Point Theory and Applications 2011, ... δ
n+1
Bx
n
)
.
Piri and Badali Fixed Point Theory and Applications 2011, 2011:55
http://www.fixedpointtheoryandapplications.com/content/2011/1/55
Page 9 of 16
RESEARC H Open Access
Strong convergence ... iterative process,
strong convergence, variational inequality
1 Introduction
Throughout this paper, we assume that H is a real Hilbert space with inner product
and norm are denoted by 〈.,.〉 and || . ||,...
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Báo cáo hóa học: "Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings" pdf
Ngày tải lên :
21/06/2014, 00:20
... product 〈·,·〉 andnorm||·||,andletC be a
closed convex subset of H.Wewritex
n
⇀ x to indicate that the sequence {x
n
}con-
verges weakly to x,andx
n
đ x implies that {x
n
} converges strongly to ... is maximal if and only if for (x, f ) ẻ H × H, 〈x-
y, f-g〉 ≥ 0 for every (y, g) Î G(T) implies f Î Tx.LetA be an inverse strongly mono-
tone mapping of C into H,andletN
C
v be t he normal cone ... article as: Bunyawat and Suantai: Strong convergence theorems for variational inequalities and fixed
points of a countable family of nonexpansive mappings. Fixed Point Theory and Applications 2011...
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Báo cáo hóa học: " A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space" pptx
Ngày tải lên :
21/06/2014, 01:20
... Banach space, and {x
n
}beasequenceinE.Wedenotebyx
n
đ x and
x
n
x the strong convergence and weak convergence of {x
n
}, respectively. The normal-
ized duality mapping J : E ® 2
E*
is defined by
J
x ... and
relatively nonexpansive mappings. Fixed Point Theory Appl 2008, 2008:11, (Article ID 528476).
9. Takahashi W, Zembayashi K: Strong and weak convergence theorems for equilibrium problems and ... x
),
which implies that
¯
u
=
x
and
f
0
= J
¯
u
. It follows from Remark 2.1(iv) and (v) that E*
has the Kadec-Klee property, and so
J
y
n
k
→ J
¯
u
by (2.4) and (2.5). By Remar k 2.1(vii)
and (ii),...
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Báo cáo hóa học: " Strong convergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions" potx
Ngày tải lên :
21/06/2014, 01:20
... is bounded, closed and con-
vex and T is a nonexpansive mapping of C into itself, then F(T) is nonem pty; for
instance, see [5]. Recently, Tada and Takahashi [6] and Takahashi and Takahashi [7]
considered ... Kangtunyakarn: Strong convergence theorem for a generalized equilibrium problem and
system of variational inequalities problem and infinite family of strict pseudo-contractions. Fixed Point Theory and
Applications ... b < 1
, and
j
1
,
j
2
, α
j
3
∈ (κ,1
)
for all j = 1, 2, . For every n ẻ N, let S
n
and S are S-mapping gener-
ated by T
n
, ,T
1
and r
n
, r
n-1
, , r
1
and T
n
, T
n-1
, , and r
n
, r
n-1
,...
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Báo cáo hóa học: " Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications" pptx
Ngày tải lên :
21/06/2014, 01:20
... closed convex subset of H and T : K đ H be a mapping.
In this paper, the set of fixed points of T is denoted by F(T). We use symbols đ and
to denote strong and weak convergence, respectively.
For ... article as: He and Du: Strong convergence theorems for equilibrium problems and fixed point
problems: A new iterative method, some comments and applications. Fixed Point Theory and Applications ... n ≥ 0
.
If
He and Du Fixed Point Theory and Applications 2011, 2011:33
http://www.fixedpointtheoryandapplications.com/content/2011/1/33
Page 2 of 15
RESEARC H Open Access
Strong convergence theorems...
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báo cáo hóa học: " Strong convergence theorems for system of equilibrium problems and asymptotically strict pseudocontractions in the intermediate sense" pot
Ngày tải lên :
21/06/2014, 02:20
... notations:
1. for the weak convergence and đ for the strong convergence.
2.
ω
w
(x
n
)={x : ∃x
n
j
x
}
denotes the weak ω-limit set of {x
n
}.
2. Preliminaries
We need some facts and tools in a real ... (2009). doi:10.1016/j.na.2008.02.090
14. Tada, A, Takahashi, W: Weak and strong convergence theorems for a nonexpansive mappingand a equilibrium
problem. J Optim Theory Appl. 133, 359–370 (2007). ... [0, 1/2] and C
2
: = (1/2, 1]. Hence,
|
T
n
x − T
n
y
| = k
n
|x −
y
|≤|x −
y
| for all x,
y
∈ C
1
and n ∈
N
and
|
T
n
x − T
n
y
| =0≤|x −
y
| for all x,
y
C
2
and n N
.
For x ẻ C
1
and y ẻ...
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Báo cáo hóa học: " Research Article A New Strong Convergence Theorem for Equilibrium Problems and Fixed Point Problems in Banach Spaces" pptx
Ngày tải lên :
21/06/2014, 05:20
... 14 Fixed Point Theory and Applications
19 W. Takahashi and Kei Zembayashi, Strong and weak convergence theorems for equilibrium
problems and relatively nonexpansive mappings ... Accretive and Monotone Type,vol.
178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Marcel Dekker, New York, NY, USA,
1996.
2 S Y. Matsushita and W. Takahashi, Weak and strong convergence ... 20–30, 2009.
15 A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and
an equilibrium problem,” Journal of Optimization Theory and Applications, vol. 133,...
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báo cáo hóa học:" Research Article Strong Convergence to Common Fixed Points for Countable Families of Asymptotically Nonexpansive Mappings and Semigroups" ppt
Ngày tải lên :
21/06/2014, 11:20
... Su and Qin 6 modified the hybrid iteration method of Nakajo and
Takahashi through the monotone hybrid method, and to prove strong convergence theorems.
In 2008, Takahashi et al. 7 proved strong ... asymptotically
nonexpansive mappings and semigroups in a Hilbert space, and to prove strong convergence
theorems. Our results presented are improvement and extension of the corresponding results
in 3, 5–8 and many authors.
2. ... with inner product ·, · and norm ·,
and we write x
n
→ x to indicate that the sequence {x
n
} converges strongly to x.LetC be
a nonempty closed convex subset of H,andletT : C → C be a mapping....
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báo cáo hóa học:" Research Article Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces" pptx
Ngày tải lên :
21/06/2014, 11:20
... Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal of
Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005.
24 W. Takahashi, Weak and strong convergence ... A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems,”
Journal of Nonlinear and Convex Analysis, vol. 9, no. 1, pp. 37–43, 2008.
15 S. Plubtieng and R. Punpaeng, ... quasi-φ-
nonexpansive mappings and equilibrium problems,” Journal of Computational and Applied Mathematics,
vol. 234, no. 3, pp. 750–760, 2010.
18 S. H. Wang, G. Marino, and F. H. Wang, Strong convergence theorems...
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