product of weak and strong convergence

... sets of all positive integers and real num- bers, respectively. Let E be a Banach space and let E* b e the dual space of E. For a sequence {x n }ofE and a point x Î E, the weak convergence of {x n }tox ... 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 of an implicit-shrinking ... 2011:96 http://www.fixedpointtheoryandapplications.com/content/2011/1/96 Page 12 of 20 RESEARC H Open Access Weak and strong convergence theorems of implicit iteration process on Banach spaces Lai-Jiu Lin 1* , Chih-Sheng Chuang 1 and Zenn-Tsun Yu 2 *...

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 Î 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 ® ... 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 of an implicit-shrinking ... 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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... 1. 1.10 The class of asymptotically κ-strict pseudocontractions was introduced by Qihou 4 in 1996 see also 5.KimandXu6 studied weak and strong convergence theorems for this class of mappings. ... 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, ... O’Regan, and D. R. Sahu, “Iterative construction of fixed points of nearly asymptotically nonexpansive mappings,” Journal of Nonlinear and Convex Analysis,vol.8,no.1,pp. 61–79, 2007. 11 G. Marino and...

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Ngày tải lên: 09/08/2014, 06:22

... rate of convergence of Picard and Mann iterations for a class of Zamfirescu operators in arbitrary Banach spaces. Popescu [28] also used this concept to compare the rate of convergence of Picard and ... the rate of convergence of W (T,N ) -iteration and K (T,N ) - iteration for continuous and nondecreasing mappings on an arbitrary interval in the 15 Table 2: Comparison of the rate of convergence ... possible to prove the convergence theorem of a finite family of continuous mappings on an arbitrary interval by using W-mappings and K-mappings and how about the rate of convergence of those methods? 24 Corollary...

Ngày tải lên: 20/06/2014, 20:20

... lement of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of Yao et al. Fixed Point Theory and Applications ... 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 ... problem that consists of finding a co mmon point that lies in the solution set of a variational inequality and the set of fixed points of a nonexpansive mapping. This type of problem aries in various...

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, ... regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for b-inverse strongly monotone ... D ® H,weletF ε (T; D) be the set of 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...

Ngày tải lên: 20/06/2014, 22:20

... element of the set of solutions of variational inequality and the set of common fixed points of a countable family of nonexpansive mappings is introduced and studied. A strong convergence theorem of ... imposed on {a n } and {l n }, the sequence {x n } generated by (1.5) converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality ... 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...

Ngày tải lên: 21/06/2014, 00:20

... common element of the set of a generalized equilibrium problem of the set of solution to a system of variational inequalities, and of the set of fixed points of an infinite family of strict pseudo- contractions. ... 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 ... class of -strict pseudo-contractions fall into the one between classes of nonex- pansive mappings and pseudo-contractions, and the class of strong pseudo-contrac- tions is independent of the...

Ngày tải lên: 21/06/2014, 01:20

... contributions PD carried out the proof of convergence of the theorems and realization of numerical examples. JZ carried out the check of the manuscript. All authors read and approved the final manuscript. Competing ... notations: 1. ⇀ for the weak convergence and ® 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 ... closed convex subset C of a real Hilbert space H. Consider the problem of finding a common element of the fixed point set of these mappings and the solution set of a system of equilibrium problems...

Ngày tải lên: 21/06/2014, 02:20

... Mappings and Semigroups Kriengsak Wattanawitoon 1, 2 and Poom Kumam 2, 3 1 Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology ... semigroups in Hilbert spaces. Our results extend and improve the recent results of Nakajo and Takahashi 2003 and of Zegeye and Shahzad 2008 from the class of nonexpansive mappings to asymptotically ... ⊂  ∞ n1 FT n , where FT N  is the set of all fixed points of T n and FT is the set of all common fixed points of T. We consider the following conditions of {T n } and T see 9: i NST-condition...

Ngày tải lên: 21/06/2014, 11:20

... element of the set of solutions of an infinite family of equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space. We prove some strong convergence ... 1. 1.25 The proof method of the main result of this paper is different with ones of others in the literatures and our result extends and improves the ones of Colao et al. 5 and some others. Fixed ... h 1 x and h 2 x are both the convex and lower semicontinuous functions defined on a closed convex subset of C of a Hilbert space H. We denote by A the set of solutions of the problem 4.1 and...

Ngày tải lên: 21/06/2014, 11:20

... possible to prove the convergence theorem of a finite family of continuous mappings on an arbitrary interval by using W-mappings and K-mappings and how about the rate of convergence of those methods? 24 Lemma ... 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 continuous ... con- cept of K-mapping for finding a common fixed point of a finite family of nonexpansive mappings and a solution of an equilibrium problem. Applications of K-mappings for fixed point problems and equilibrium...

Ngày tải lên: 21/06/2014, 17:20

... “Regularization of nonlinear ill-posed variational inequalities and convergence rates,” Set-Valued Analysis, vol. 6, no. 4, pp. 313–344, 1998. 7 K. Nakajo and W. Takahashi, Strong and weak convergence ... 4496–4503, 2008. 19 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, ... element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically nonexpansive mappings. Our results improve and extend the results...

Ngày tải lên: 21/06/2014, 20:20