linear operators in hilbert spaces

... imply that P x0 y0 Finding zeroes of maximal monotone operators is the central and important topic in nonlinear functional analysis A classical method to solve the following set-valued equation: ... sequence {en } in Hilbert spaces For this purpose, we collect some lemmas that will be used in the proof of the main results in the next section The first lemma is standard and it can be found in some ... Takahashi, “Iterative schemes for approximating solutions of relations involving accretive operators in Banach spaces, ” in Fixed Point Theory and Applications, Vol 5, Y J Cho, J K Kim, and S M Kang,...

Ngày tải lên: 22/06/2014, 06:20

... iterations in a Hilbert space,” Mathematical Programming, vol 87, no 1, pp 189–202, 2000 [7] S Kamimura and W Takahashi, “Approximating solutions of maximal monotone operators in Hilbert spaces, ” ... problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality Preliminaries Recall that a mapping U : H ... Mathematics, Tianjin Polytechnic University, Tianjin 300160, China Email address: yuyanrong@tjpu.edu.cn Rudong Chen: Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China Email...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 05/08/2014, 09:46

... quasi-nonexpansive mappings in Hilbert spaces Comput Math Appl 59(1), 74–79 (2009) Tian, M: A general iterative algorithm for nonexpansive mappings in Hilbert spaces Nonlinear Anal 73, 689–694 ... scheme for nonexpansive mappings in Hilbert spaces 2010 International Conference on Computational Intelligence and Software Engineering, CiSE 2010 (2010) art no 5677064 Maingé, PE: Strong convergence ... sequence {an} satisfies certain conditions: x∈C Ax, x − x, b , (1:3) where C is the set of fixed points set of T on H and b is a given point in H In 2006, Marino and Xu [3] combined the iterative method...

Ngày tải lên: 20/06/2014, 22:20

... nonexpansive mappings in a Hilbert space In 2008, Kohsaka and Takahashi [6] introduced nonspreading mapping and obtained a fixed point theorem for a single nonspreading 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 ... nonspreading mappings Recently, Takahashi and Yao [9] proved the following nonlinear ergodic theorem for nonspreading mappings in Hilbert spaces Furthermore, Takahashi and Yao [9] also introduced...

Ngày tải lên: 20/06/2014, 22:20

... convergence principle for Fejér-monotone methods in Hilbert spaces Math Oper Res 26, 248–264 (2001) doi:10.1287/moor.26.2.248.10558 Solodov, MV, Svaiter, BF: Forcing strong convergence of proximal point ... strong convergence of proximal point iterations in a Hilbert space Math Programming Ser 87, 189–202 (2000) Xu, HK: Iterative algorithms for nonlinear operators J Lond Math Soc 66, 240–256 (2002) ... contraction-proximal point algorithms in hilbert spaces Journal of Inequalities and Applications 2011 2011:41 Submit your manuscript to a journal and benefit from: Convenient online submission Rigorous...

Ngày tải lên: 21/06/2014, 00:20

... one Related to the variational inequalities, we have the problem of finding the fixed points of the nonlinear mappings, which is the subject of current interest in functional analysis It is natural ... definitions Definition2.1 Let A: H ® H be a mapping and K ⊂ H Then, A is said to be semicontinuous at a point x in K if lim A(x + th), y = A(x), y , x + th ∈ K, y ∈ H t→0 Definition2.2 A mapping ... http://www.journalofinequalitiesandapplications.com/content/2011/1/21 Page of 11 monotone mapping, T: K ® H be l-inverse strongly monotone mapping If g is an expanding affine continuous mapping and GVIK(A,...

Ngày tải lên: 21/06/2014, 01:20

... A system of nonlinear variational inequalities involving strong monotone and pseudocontractive mappings Adv Nonlinear Var Inequal 6, 91–99 (2003) Noor, MA: General variational inequalities Appl ... presented in Lemma 1.6 plays an important role in developing the numerical methods for solving the system of general nonlinear set-valued mixed variational inequalities problems In fact, assuming that ... doi:10.1007/s00186-007-0207-4 Inchan, I, Petrot, N: System of general variational inequalities involving different nonlinear operators related to fixed point problems and its applications Fixed Point Theory Appl...

Ngày tải lên: 21/06/2014, 01:20

... pseudo-contractions in Hilbert spaces, ” Nonlinear Analysis: Theory, Methods & Applications, vol 69, no 2, pp 456–462, 2008 14 F E Browder and W V Petryshyn, “Construction of fixed points of nonlinear mappings in ... mappings and inversestrongly monotone mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol 61, no 3, pp 341–350, 2005 12 P L Combettes and S A Hirstoaga, “Equilibrium programming in ... Notes in Econom and Math Systems, pp 187–201, Springer, Berlin, Germany, 1999 S Plubtieng and R Punpaeng, “A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, ”...

Ngày tải lên: 21/06/2014, 05:20

... theorems are established in real Hilbert spaces In order to prove our main results, we also need the following lemmas Lemma 1.4 In a real Hilbert space, the following inequality holds: ax 1−a ... in the intermediate sense, then T has a fixed point It is worth mentioning that the class of mappings which are asymptotically nonexpansive in the intermediate sense may not be Lipschitz continuous; ... 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

... non -linear mappings in Banach spaces, ” Archive for Rational Mechanics and Analysis, vol 24, pp 82–90, 1967 F E Browder, “Nonlinear operators and nonlinear equations of evolution in Banach spaces, ” ... be 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 ∗ The mapping f with ... point in C In 1968, Browder proved the existence results of zero points for maximal monotone mappings in reflexive Banach spaces To be more precise, he proved the following theorem Fixed Point...

Ngày tải lên: 21/06/2014, 07:20

... the pairing between E and E∗ Let A1 , A2 : E → E be single-valued nonlinear mappings, and let M1 , M2 : E → 2E set-valued nonlinear mappings We consider a system of quasivariational inclusions ... nonexpansive mappings in Banach spaces, ” Nonlinear Analysis: Theory, Methods & Applications, vol 70, no 1, pp 45–57, 2009 34 P L Combettes and S A Hirstoaga, “Equilibrium programming in Hilbert spaces, ” ... combinations of sunny nonexpansive retractions,” Topological Methods in Nonlinear Analysis, vol 2, no 2, pp 333–342, 1993 41 H.-K Xu, “Inequalities in Banach spaces with applications,” Nonlinear...

Ngày tải lên: 21/06/2014, 07:20

... mapping pseudocontractive mapping, resp The results presented in this paper improve and generalize some corresponding results in 4–6 Fixed Point Theory and Applications Preliminaries A mapping ... semigroup in Hilbert space,” Nonlinear Analysis: Theory, Methods & Applications, vol 70, no 9, pp 3065–3071, 2009 G Marino and H.-K Xu, “A general iterative method for nonexpansive mappings in Hilbert ... nonexpansive semigroup satisfying 3.22 and F Γ is a singleton {θ}, where θ 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...

Ngày tải lên: 21/06/2014, 07:20

... of nonlinear mappings is an important and active research area In particular, iterative algorithms for finding fixed points of nonexpansive mappings have received vast investigation cf 1, since ... nonexpansive mapping In a real Hilbert space H, we have x−y x y − x, y , ∀x, y ∈ H 2.2 In order to prove our main results, we need the following lemmas Lemma 2.1 see 13 Let H be a Hilbert space, ... strongly to a fixed point x∗ of T which solves the variational inequality: Ax∗ , x∗ − u ≤ 0, Setting F u∈F T 3.17 I, the identity mapping, in Theorem 3.1, we can obtain the following result Corollary...

Ngày tải lên: 21/06/2014, 11:20

... nonlinear operators, ” Journal of the London Mathematical Society, vol 66, no 1, pp 240–256, 2002 23 P L Combettes and S A Hirstoaga, “Equilibrium programming in Hilbert spaces, ” Journal of Nonlinear ... mappings and inversestrongly monotone mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol 61, no 3, pp 341–350, 2005 21 W Takahashi, Nonlinear Functional Analysis, Fixed Point ... point, A be a strongly positive linear bounded operator on H and {T }N be a finite family of nonexpansive mappings of H into itself such that F n N n F Tn / ∅ In 2003, Xu introduced the following...

Ngày tải lên: 21/06/2014, 11:20

... 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 introduced a new mapping, called Kmapping, for finding ... K-mapping of C into itself generated by T1 , , TN and λ1 , , λN Then F K i F Ti Fixed Point Theory and Applications By using the same argument as in 9, Lemma 2.10 , we obtain the following ... nonexpansive mappings {Ti }N1 , which i solves a variational inequaility problem 4 Fixed Point Theory and Applications In order to prove our main results, we need the following lemmas Lemma...

Ngày tải lên: 21/06/2014, 11:20

... nonexpansive mappings in Hilbert spaces, ” Nonlinear Analysis, vol 54, no 8, pp 1417–1426, 2003 L P Belluce and W A Kirk, “Nonexpansive mappings and fixed-points in Banach spaces, ” Illinois Journal ... Therefore we obtain limn αn /tn 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 {αn } and {tn } be sequences in R satisfying (C1) ... E be a Hilbert space Let {xn } be a sequence in E converging weakly to z0 ∈ H Then the inequality lim infn xn − z ≤ lim infn xn − z0 implies z z0 We generalize Theorem 1.2 4 Fixed Point Theory...

Ngày tải lên: 21/06/2014, 20:20

... ≥ for all u ∈ C and hence w ∈ EP(B) Since Hilbert spaces are Opial’s spaces, from (3.22), we have liminf yni − w ≤ liminf Syni − Sw ≤ liminf yni − w < liminf yni − Sw , n→∞ n→∞ n→∞ n→∞ (3.27) ... point problems in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol 331, no 1, pp 506–515, 2007 [4] F Deutsch and I Yamada, “Minimizing certain convex functions over the intersection ... Natural Science Foundation of China under Grant no 10771050 References [1] P L Combettes and S A Hirstoaga, “Equilibrium programming in Hilbert spaces, ” Journal of Nonlinear and Convex Analysis, vol...

Ngày tải lên: 21/06/2014, 22:20