pythagorean theorem in hilbert space

... convergence theorem of fixed points is established in the framework of Hilbert spaces. 1. Introduction and Preliminaries Throughout this paper, we always assume that H is a real Hilbert space, whose inner ... Asymptotically Pseudocontractive Mappings in Hilbert Spaces Xiaolong Qin, 1 Sun Young Cho, 2 and Shin Min Kang 3 1 School of Mathematics and Information Sciences, North China University of Water Resources ... pseudocontractions was introduced by Browder and Petryshyn 11 in a real Hilbert space. In 2007, Marino and Xu 12 obtained a weak convergence theorem for the class of strictly pseudocontractive mappings; see...

Ngày tải lên: 21/06/2014, 05:20

... quasi-nonexpansive mappings in Hilbert spaces Ming Tian * and Xin Jin * Correspondence: tianming1963@126.com College of Science, Civil Aviation University of China, Tianjin 300300, China Abstract In this article, ... quasi-nonexpansive mapping, Lipschitzian continuous, strongly mono- tone, nonlinear operator, fixed point, viscosity method 1. Introduction Let H be a real Hilbert space with inner product 〈·,·〉, and induced ... quasi-nonexpansive mappings in Hilbert spaces. Comput Math Appl. 59(1), 74–79 (2009) 5. Tian, M: A general iterative algorithm for nonexpansive mappings in Hilbert spaces. Nonlinear Anal. 73, 689–694...

Ngày tải lên: 20/06/2014, 22:20

... mappings in a Hil- bert space. In 2008, Kohsaka and Takahashi [6] introduced nonspreading mapping and obtained a fixe d point theorem for a single nonspr eading mapping and a common fixed point theorem ... following fixed point theorems for nonexpansive mappings in Hilbert spaces. In 1965, Browder [1] gave the following demiclosed principle for nonexpansive map- pings in Hilbert spaces. Theorem 1.1. ... nonspreading mapping in Hilbert spaces. In 2010, Takahashi [7] extended Ray’ s type theorem for nonspreading mapping in Hilbert spaces. Iemoto and Takahashi [8] also extended the demiclosed principles...

Ngày tải lên: 20/06/2014, 22:20

... contraction-proximal point algorithms in hilbert spaces. Journal of Inequalities and Applications 2011 2011:41. Submit your manuscript to a journal and benefi t from: 7 Convenient online submission 7 ... freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com Wang and Wang Journal of Inequalities and ... University, Luoyang 471022, China Abstract We consider the relaxed and contraction-proximal point algorithms in Hilbert spaces. Some conditions on the parameters for gu aranteeing the convergence of...

Ngày tải lên: 21/06/2014, 00:20

... mappings in a Hil- bert space. In 2008, Kohsaka and Takahashi [6] introduced nonspreading mapping and obtained a fixe d point theorem for a single nonspr eading mapping and a common fixed point theorem ... nonspreading mapping in Hilbert spaces. In 2010, Takahashi [7] extended Ray’ s type theorem for nonspreading mapping in Hilbert spaces. Iemoto and Takahashi [8] also extended the demiclosed principles ... 1.1. The class of asymptotic nonspreading mappings contains the class of nonspreading mappings and the class of TJ-2 mappings in a Hilbert space. Indeed, in Definition 1.1, we know that (i) if a...

Ngày tải lên: 21/06/2014, 00:20

... hemicontinuous mapping and inverse strongly monotone mappings in Hilbert spaces. J Inequal Appl 10 (2010). Article ID 451916 10. Osilike, MO, Udomene, A: Demiclosedness principle and convergence theorems ... reproduction in any medium, provided the original work is properly cited. monotone mapping, T: K ® Hbel-inverse strongly monotone mapping. If g is an expanding affine continuous mapping and GVI K (A, ... one. Related to the variational inequalities, we have the pro blem of finding the fixed points of the nonlinear mappings, which is the subject of current interest in function al analysis. It is...

Ngày tải lên: 21/06/2014, 01:20

... announced in [1] is very interesting. (III) If A, B : H ® H are single-valued mappings, then, from the problem (1.1), we have the following system of general nonlinear mixed variational inequalities ... system of nonlinear variational inequalities involving strong monotone and pseudocontractive mappings. Adv Nonlinear Var Inequal. 6,91–99 (2003) 6. Noor, MA: General variational inequalities. ... single-valued mappings to set-valued mappings, and hence include several related problems as spacial cases. We need the following basic concepts and well-known results: Definition 1.1. A mapping...

Ngày tải lên: 21/06/2014, 01:20

... Strict Pseudocontractions in Hilbert Spaces Ming Tian College of Science, Civil Aviation University of China, Tianjin 300300, China Correspondence should be addressed to Ming Tian, tianming1963@126.com Received ... pseudocontraction mapping in the setting of real Hilbert spaces. We proved strong convergence theorems of the sequence generated by our proposed schemes. 1. Introduction Let H be a real Hilbert space and ... “Equilibrium programming in Hilbert spaces,” Journal of Nonlinear and Convex Analysis. An International Journal, vol. 6, no. 1, pp. 117–136, 2005. 13 H. Zhou, “Convergence theorems of fixed points for κ-strict...

Ngày tải lên: 21/06/2014, 05:20

... a mapping of a linear normed space X into its dual space X ∗ . T is said to be hemicontinuous if it is continuous from each line segment in X to the weak topology in X ∗ . 7 The mapping f with ... Maximal Monotone Mappings in Hilbert Spaces Yuan Qing, 1 Xiaolong Qin, 1 Haiyun Zhou, 2 and Shin Min Kang 3 1 Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China 2 Department ... monotone mappings in the framework of real Hilbert spaces. 2. Main Results Lemma 2.1. Let C be a nonempty closed convex subset of a Hilbert space H and T : C → H a demicontinuous monotone mapping. Then...

Ngày tải lên: 21/06/2014, 07:20

... satisfying 3.22 and FΓ is a singleton {θ},whereθ is the zero point in H. Combining the proofs of Theorems 3.2 and 3.6, we can easily conclude the following result. Theorem 3.8. Let f : H → H be ... points of a nonexpansive semigroup in Hilbert spaces. The results presented in this paper improve and generalize some corresponding results in X. Li et al., 2009, S. Li et al., 2009, and Marino ... nonexpansive mappings. Thus, we have the following mean ergodic assertions of general viscosity iteration process for nonexpansive mappings in Hilbert spaces. Corollary 3.4. Let H, f, A be as in Theorem...

Ngày tải lên: 21/06/2014, 07:20

... {T n } 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. Corollary ... a fixed point x ∗ of T which solves the variational inequality:  Ax ∗ ,x ∗ − u  ≤ 0,u∈ F  T  . 3.17 Setting F  I, the identity mapping, in Theorem 3.1, we can obtain the following result. Corollary ... 3.25 Fixed Point Theory and Applications 7 Setting F  A in Theorem 3.1, we can obtain the following result. Corollary 3.2. Let C be a nonempty closed convex subset of a real Hilbert space H.LetT...

Ngày tải lên: 21/06/2014, 11:20

... Method for In nite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces Shenghua Wang 1, 2 and Baohua Guo 1, 2 1 National Engineering Laboratory ... space. In this paper, we consider a new iterative scheme for obtaining a common element in the solution set of an in nite family of generalized equilibrium problems and in the common fixed-point ...   N n1 FT n . 6 Fixed Point Theory and Applications 2. Preliminaries Let C be a closed convex subset of a Hilbert space H. For any point x ∈ H, there exists a unique nearest point in C, denoted by P C x,...

Ngày tải lên: 21/06/2014, 11:20

... original work is properly cited. We introduce a new general iterative method by using the K-mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert ... well-defined and Theorem 2.1 8 is obtained. In the case C /  H, we have to modify the iterative scheme 1.8 in order to make it well-defined. In 2009, Kangtunyakarn and Suantai 9 introduced a new mapping, ... K- mapping, for finding a common fixed point of a finite family of nonexpansive mappings. For a finite family of nonexpansive mappings {T i } N i1 and sequence {γ n,i } N i in 0, 1, the mapping K n :...

Ngày tải lên: 21/06/2014, 11:20

... 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 method in a Hilbert space and ... In nitely Nonexpansive Mappings in Hilbert Space Yi-An Chen College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China Correspondence should be ... distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Let C be a nonempty closed convex subset of a Hilbert space H, T a self-mapping of C. Recall that...

Ngày tải lên: 21/06/2014, 20:20

... obtain lim n α n /t n  0. By Theorem 2.3 and Example 2.5, we obtain the following. Theorem 2.6. Let E be an in nite-dimensional Hilbert space. Let {α n } and {t n } be sequences in R satisfying ... non-linear mappings in Banach spaces,” Archive for Rational Mechanics and Analysis, vol. 24, pp. 82–90, 1967. 4 S. Reich, “Weak convergence theorems for nonexpansive mappings in Banach spaces,” ... finding nearest common fixed points of nonexpansive mappings in Hilbert spaces,” Nonlinear Analysis, vol. 54, no. 8, pp. 1417–1426, 2003. 7 L. P. Belluce and W. A. Kirk, “Nonexpansive mappings...

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