weak and strong convergence in hilbert spaces

... introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. ... point of S. Motivated by Kohsaka and Takahashi [7], and Reich [13], our purpose in this paper is to prove weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces ... WEAK AND STRONG CONVERGENCE THEOREMS FOR RELATIVELY NONEXPANSIVE MAPPINGS IN BANACH SPACES SHIN-YA MATSUSHITA AND WATARU TAKAHASHI Received 29 October 2003 We first introduce an iterative

Ngày tải lên: 23/06/2014, 00:20

... B(S) containing 1 and let µ be a mean on X.Letf be a mapping from S into E such that { f (t):t ∈ S} is contained in a weakly compact convex subset of E and the mapping t →f (t),x ∗  is in X for ... the strong convergence of the iterations in a uniformly convex Banach space, requiring one mapping T i in the family to be semi compact. Copyright © 2005 Hindawi Publishing Corporation Fixed Point ... semicompact, then {x n } converges strongly to a fixed point of T. 352 Weak and strong convergence theorems Theorem 5.4. Let T and U be commutative nonexpansive mappings from C into itself such that F(T)

Ngày tải lên: 23/06/2014, 00:20

... others. 1. Introduction and Preliminaries Throughout this paper, we always assume that H is a real Hilbert space with inner product ·, · and norm ·.? ?and → denote weak and strong convergence, ... mappings, ” Journal of Nonlinear and Convex Analysis, vol 8, no 1, pp 61–79, 2007 11 G Marino and H.-K Xu, Weak and strong convergence theorems for strict pseudo-contractions in ... Pseudocontractive Mappings in the Intermediate Sense Jing Zhao 1, 2 and Songnian He 1, 2 1 College of Science, Civil Aviation University of China, Tianjin 300300, China 2 Tianjin Key Laboratory For

Ngày tải lên: 21/06/2014, 11:20

... Shioji and Takahashi 13, and Tan and Xu 14 in the settings of Hilbert spaces and uniformly convex Banach spaces. There are many methods for approximating fixed points of a nonexpansive mapping. ... nonexpansive mappings, due to Xu and Ori, to the case of asymptotically quasi-nonexpansive mappings in a setting of Banach spaces. In 17 it has been studied the weak and strong convergence of ... I-nonexpansive mappings which is asymptotically I-nonexpansive. In 21 a weakly convergence theorem for I-asymptotically quasi-nonexpansive mapping defined in Hilbert space was proved. In 22 strong convergence

Ngày tải lên: 21/06/2014, 20:20

... nonexpansive mappings is introduced and strong and weak convergence theorems of this scheme to common fixed point of asymptotically non- expansive mappings are proved. In particular, our weak convergence ... [13] introduced a three-step iterative scheme and studied the approximate so- lution of variational inclusion in Hilbert spaces by using the techniques of updating the solution and auxiliary principle. ... important and significant role in solving various problems which arise in pure and applied sciences. Re- cently, Xu and Noor [5] introduced and studied a three-step scheme to approximate fixed points

Ngày tải lên: 22/06/2014, 19:20

... nonexpansive nonself-mappings (when such a fixed point exists) and gave some strong and weak convergence theorems for such mappings. Inspired and motivated by these facts, we introduce and study a multistep ... nonexpansive mappings in Banach spaces. Recently, Khan and Fukhar-ud-din [6] extended their scheme to the modified Ishikawa iterative schemes with errors for two mappings and gave weak and strong convergence ... Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006, Article ID 81493, Pages 1–12 DOI 10.1155/FPTA/2006/81493 2 Weak and strong convergence approximating a fixed point

Ngày tải lên: 22/06/2014, 22:20

... multivalued nonexpansive mapping; hybrid subgradient method; fixed point; weak and strong convergence Introduction Let H be a real Hilbert space with inner product ·, · and norm · , respectively ... Equilibrium programming in Hilbert spaces J Nonlinear Convex Anal 6, 117-136 (2005) Facchinei, F, Pang, JS: Finite-Dimensional Variational Inequalities and Complementarity Problems Springer, New York ... equilibrium problems and a finite family of multivalued nonexpansive mappings, but also to establish weak and strong convergence theorems involving only one projection rather than two as in the extragradient

Ngày tải lên: 16/12/2017, 15:19

... L 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 ... Iterative Method for In? ??nite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces Shenghua Wang1, and Baohua Guo1, National Engineering Laboratory for ... and few of authors investigate the in? ??nite family of equilibrium problems in a Hilbert space or Banach space In this paper, we consider a new iterative scheme for obtaining a common element in

Ngày tải lên: 21/06/2014, 11:20

... problems and fixed point problems in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol 331, no 1, pp 506–515, 2007 7 F Deutsch and I Yamada, “Minimizing certain convex... ... element of the set of fixed points of a non-self nonexpansive mapping and the set of solutions of the equilibrium problem and obtained a strong convergence theorem in a real Hilbert space. Iterative ... frequently in various areas of mathematical sciences and engineering. For example, the well-known convex feasibility problem reduces to finding a point in the intersection of the fixed-point sets

Ngày tải lên: 22/06/2014, 03:20

... study of certain integral representation formulas, in particular in the analytic functional calculus for several commuting operators in Hilbert spaces These integral kernels are obtained in connection ... ,ằ,,) instead of dz = (dz,, .,dz,,) in order to stress the independence of the former on the points in Q.) As in the scalar case, the operator @ is closed and densely defined In fact, if Ạ is in ... operator on Hilbert spaces of square integrable vector-valued exterior forms Let H be a complex Hilbert space and @(H)((H)) the set of all densely defined closed (bounded) operators, acting in H For

Ngày tải lên: 05/08/2014, 09:46

... complete convergence for sequences of coordinatewise negatively associated random vectors in Hilbert spaces Nguyen Van Huan∗ Department of Mathematics and Applications, Saigon University, Ho Chi Minh ... Quang), tranthuandhv@gmail.com (Nguyen Tran Thuan) Preprint submitted to Elsevier July 25, 2013 1. Introduction Hsu and Robbins [7] introduced the concept of complete convergence and proved that ... denotes the cardinality of A. An infinite family of random variables is NA if every finite subfamily is NA. 2 As in Ko et al. [9], a finite family {Xi , 1 i n} of Rd -valued random vectors is

Ngày tải lên: 16/10/2015, 09:29

... applied, and engineering sciences. For more information and results on the general variational inequalities problems, one may consult [2-18]. Inspired and motivated by the recent research going on in ... -strongly monotone and Lipschitz continuous mapping with a constant τ A and B : H ® CB(H) be ν B -strongly monotone and Lipschitz c ontinuous mapping with a constant τ B .Letg: H ® Hbeν g -strongly ... be a real Hilbert space. Let A : H ® Hbeν A -strongly monotone and Lipschitz cont inuous mapping with a constant τ A ,andB: H ® Hbeν B -strongly monotone and Lipschitz continuous mapping with

Ngày tải lên: 21/06/2014, 01:20

... nonexpansive semigroup, and from contraction mapping to φstrongly pseudocontractive mapping and pseudocontractive mapping, respectively... nonexpansive mappings in Hilbert spaces, ” Journal of ... : {Tt : t ≥ 0} and φ-strongly pseudocontractive mapping pseudocontractive mapping, resp. in Hilbert spa ces. On the other hand, we consider the convergence of the following general viscosity ... and f is a φ-strongly pseudocontractive mapping pseudocontractive mapping, resp.. The results presented in this paper improve and generalize some corresponding results in 4–6. 4 Fixed Point

Ngày tải lên: 21/06/2014, 07:20

... 11 Y Yao, Y C Liou, and G Marino, ? ?Strong convergence of two iterative algorithms for nonexpansive mappings in Hilbert spaces, ” Fixed Point Theory and. .. integrals,” Journal ... } by {W n } in the recursion formula 3.19, we can obtain the corresponding results of the so-called W-mapping. Setting F  A and T n  T in Theorem 3.5, we can obtain the following result. ... x≥0, x ∈ FT. In this paper, motivated and inspired by the above results, we introduce two new algorithms 3.3 and 3.13 for a countable family of nonexpansive mappings in Hilbert spaces. We prove

Ngày tải lên: 21/06/2014, 11:20

... Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces Yeol Je Cho, 1 Shin Min Kang, 2 and Haiyun Zhou 3 1 Department of Mathematics Education and the RINS, Gyeongsang ... distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction and preliminaries Let H be a real Hilbert space with the inner product ·, · and norm ·. ... Kamimura, S. H. Khan, and W. Takahashi, “Iterative schemes for approximating solutions of relations involving accretive operators in Banach spaces, ” in Fixed Point Theory and Applications, Vol.

Ngày tải lên: 22/06/2014, 06:20

... Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces Yeol Je Cho, 1 Shin Min Kang, 2 and Haiyun Zhou 3 1 Department of Mathematics Education and the RINS, Gyeongsang ... distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction and preliminaries Let H be a real Hilbert space with the inner product ·, · and norm ·. ... Kamimura, S. H. Khan, and W. Takahashi, “Iterative schemes for approximating solutions of relations involving accretive operators in Banach spaces, ” in Fixed Point Theory and Applications, Vol.

Ngày tải lên: 22/06/2014, 18:20

... and uniqueness of solutions (see e.g p 187-189]) An interesting problem studied in the qualitative theory of solutions of ordinary differential equations is to find conditions such that (1) and ... fe re n tia l equations in Hilbert, spaces Besides, we d iscu ss the relatio n between p ro p ­ erties o f solutions o f differential equations of tria n g u la r fo r m and those, o f truncated ... (see [2, 7Ị) I I M ain R esults We assume in this section the following conditions: f ( t , p mx) = p mf ( t , p mx), •>ï —p Ỉ' 7íĩ*e)ì (5) (6 ) (V* /?+, Vm € J, Vx € H ) Definition 2.1 Differential

Ngày tải lên: 14/12/2017, 19:52

... to a point in In [15], Gă uler showed that, in general, it converges weakly in infinite dimensional Hilbert spaces In order to obtain a strongly convergent sequence from the proximal point algorithm, ... forward-backward splitting methods in Hilbert spaces Main Results First, we prove the following result Theorem 3.1 Let H, B and A be as in Lemma 2.4 with D(A) = H and let F be an η-strongly monotone and γ˜ -strictly ... studied in this paper, is to find a zero p of the following variational inclusion ∈ T p, T = A + B, (1.1) where A and B are maximal monotone and A is single valued in a real Hilbert space H with inner

Ngày tải lên: 28/06/2021, 11:02

... 11 10. Xu, HK: Inequalities in Banach spaces with applications. Nonlinear Anal. 16, 1127–1138 (1991). doi:10.1016/0362-546X(91) 90200-K 11. Schu, J: Weak and strong convergence to fixed points of asymptotically ... strong convergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strong convergence ... different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem concerning two nonexpansive mappings and the resolvent...

Ngày tải lên: 20/06/2014, 21:20

... quasinonexpansive mapping. However, the converse may be false [1, Example 2]. Construction of approximating fixed points of nonlinear mappings is an important subject in the theory of nonlinear mappings and its ... c n = Lin et al. Fixed Point Theory and Applications 2011, 2011:96 http://www.fixedpointtheoryandapplications.com/content/2011/1/96 Page 14 of 20 12. James, RC: Inner products in normed linear spaces. ... 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 ®...

Ngày tải lên: 20/06/2014, 21:20