weak implies strong convergence

... conditions of strong convergence theorem are different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem ... Takahashi, W: Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces. Fixed Point Theory Appl 37–47 (2004). 2004 21. Matsushita, S, Takahashi, W: A strong convergence ... we first consider weak convergence theorems of implicit iterative processes for two nonexpansive mappings and a mapping which satisfies condition (C). Next, we consider strong convergence theorem...

Ngày tải lên: 20/06/2014, 21:20

... conditions of strong convergence theorem are different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem ... Takahashi, W: Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces. Fixed Point Theory Appl 37–47 (2004). 2004 21. Matsushita, S, Takahashi, W: A strong convergence ... we first consider weak convergence theorems of implicit iterative processes for two nonexpansive mappings and a mapping which satisfies condition (C). Next, we consider strong convergence theorem...

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... amendment process. I call the new model of judicial review weak- form judicial review, in con- trast with the strong form of judicial review in the United States. Strong- form review itself has numerous variants. ... provide a measure of the degree to which the HRA creates a weak or strong form of judicial review. The HRA system would be indistinguishable from strong- form review if statutes that courts declared ... States as weak- form. The contemporary Supreme Court certainly re- gards judicial review as having the strong form, and much of the public ap- pears to agree. 40 Exactly when we got strong- form...

Ngày tải lên: 07/03/2014, 02:20

... W: Weak and strong convergence theorems for families of nonexpansive mappings and their applications. Ann. Univ. Mariae Curie-Sklodowska 51, 277–292 (1997) [21] Takahashi, W, Shimoji, K: Convergence ... sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval. J. Math. Anal. Appl. 323, 1383–1386 (2006) [8] Atsushiba, S, Takahashi, W: Strong convergence theorems for ... sufficient condition for the strong convergence of the proposed iterative methods for continuous map- pings on an arbitrary interval is given. We also compare the rate of convergence of those iterations....

Ngày tải lên: 20/06/2014, 20:20

... Xu, HK: Strong convergence of the CQ method for fixed point processes. Nonlinear Anal. 64, 2400–2411 (2006). doi:10.1016/j.na.2005.08.018 28. Ceng, LC, Hadjisavvas, N, Wong, NC: Strong convergence ... doi:10.1007/s10898-009-9454-7 29. Opial, Z: Weak convergence of the sequence of successive approximations of nonexpansive mappings. Bull Am Math Soc. 73, 595–597 (1967) 30. Shimoji, K, Takahashi, W: Strong convergence to ... Xu, HK, Kim, TH: Convergence of hybrid steepest-descent methods for variational inequalities. J Optimiz Theory Appl. 119(1), 185–201 (2003) 10. Takahashi, W, Toyoda, M: Weak convergence theorems...

Ngày tải lên: 20/06/2014, 22:20

... ε-approximate fixed points of T, i.e., F ε (T; D)={x Î D :||x - T x || ≤ ε }. Weak convergence is denoted by ⇀ and strong convergence is denoted by ®. 3 Main results Theorem 3.1 Let S be a semigroup, ... solutions of variational inequality for b-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common ... implica- tion holds: x n → u ∈ C, Tx n → vim p l y Tu = v , where ® (resp. ⇀) denotes strong (resp. weak) convergence. Lemma 2.2 [17]LetCbeanonemptyclosedconvexsubsetofaHilbertspaceHand suppose...

Ngày tải lên: 20/06/2014, 22:20

... subset of H.Wewritex n ⇀ x to indicate that the sequence {x n }con- verges weakly to x,andx n ® x implies that {x n } converges strongly to x. For every point x Î H, there exists a unique nearest poi ... A strong convergence theorem of the proposed iterative scheme to a common fixed point of a countable family of nonexpansive mappings and a solution of variational inequality of an inverse strongly ... C, f is a contraction, A is a strongly positive lin- ear bounded operator, T n is a countable family of nonexpansive mappings of C into itself, B is a b-inverse strongly monotone mapping, {a n }...

Ngày tải lên: 21/06/2014, 00:20

... Strong convergence theorem for a generalized equilibrium problem and a k-strict pseudocontraction in Hilbert spaces. Appl Math Mech , English 2009, 30(6):685-694. 4. Peng JW, Yao JC: Strong convergence ... be a real Banach space, and {x n }beasequenceinE.Wedenotebyx n ® 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 ... Fixed Point Theory Appl 2008, 2008:11, (Article ID 528476). 9. Takahashi W, Zembayashi K: Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach...

Ngày tải lên: 21/06/2014, 01:20

... doi:10.1016/j.na.2008.02.042 4. Iiduka, H, Takahashi, W: Weak convergence theorem by Ces’aro means for nonexpansive mappings and inverse-strongly monotone mappings. J Nonlinear Convex Anal. 7, ... Math Anal Appl. 20, 197–228 (1967). doi:10.1016/0022-247X(67)90085-6 9. Marino, G, Xu, HK: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J Math Anal Appl. ... strict pseudo- contractions. Strong convergence theorem of the purposed iteration is established in the framework of Hilbert spaces. Keywords: nonexpansive mappings, strongly positive operator,...

Ngày tải lên: 21/06/2014, 01:20

... paper, the set of fixed points of T is denoted by F(T). We use symbols ® and ⇀ to denote strong and weak convergence, respectively. For each point x Î H, there exists a unique nearest point in ... Nonlinear Anal. 69, 2709–2719 (2008). doi:10.1016/j.na.2007.08.045 9. Tada, A, Takahashi, W: Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J Optim Theory ... expansive. (2) v-strongly monotone if there exists a constant v>0 such that Tx − T y , x − y ≥v||x − y || 2 , ∀x, y ∈ C . Clearly, any v-strongly monotone mapping is v-expansive. (3) u-inverse strongly...

Ngày tải lên: 21/06/2014, 01:20

... obtain strong conver- gence theorems that extend and improve the corresponding results [3,4,13,14]. We will adopt the following notations: 1. ⇀ for the weak convergence and ® for the strong convergence. 2. ω w (x n )={x ... Nonlinear Anal. 70, 1902–1911 (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 ... HK: Weak and srong convergence theorems for strict pseudo-contractions in Hlibert spaces. J Math Anal Appl. 329, 336–346 (2007). doi:10.1016/j.jmaa.2006.06.055 11. Takahashi, S, Takahashi, W: Strong...

Ngày tải lên: 21/06/2014, 02:20

... Takahashi, Strong convergence of a proximal-type algorithm in a Banach space,” SIAM Journal on Optimization, vol. 13, no. 3, pp. 938–945, 2002. 24 F. Kohsaka and W. Takahashi, Strong convergence ... 14 Fixed Point Theory and Applications 19 W. Takahashi and Kei Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings i n Banach ... pp. 15–50, Marcel Dekker, New York, NY, USA, 1996. 2 S Y. Matsushita and W. Takahashi, Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces,” Fixed Point...

Ngày tải lên: 21/06/2014, 05:20

... 4. We will use the following notations: 1  for weak convergence and → for strong convergence; 2 ω w x n {x : ∃x n j x} denotes the weak ω-limit of {x n }. We need some facts and tools ... Universities Grant ZXH2009D021. References 1 H. H. Bauschke and P. L. Combettes, “A weak- to -strong convergence principle for Fej ´ er-monotone methods in Hilbert spaces,” Mathematics of Operations ... Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990. 6 C. Martinez-Yanes and H K. Xu, Strong convergence of the CQ method for fixed point iteration processes,” Nonlinear Analysis. Theory,...

Ngày tải lên: 21/06/2014, 05:20