find uniform convergence of sequence of functions

... method of Xu 2006 and Matsushita and Takahashi 2008 , we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence ... convex subset of a uniformly convex Banach space E and ∞ let {Sn } be a family of nonexpansive mappings of C into itself with F n F Sn / ∅ Let {βn,k : n, k ∈ N, ≤ k ≤ n} be a sequence of real numbers ... fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach

Ngày tải lên: 21/06/2014, 20:20

... of at most one point, where coD is the closure of the convex hull of D. 8 Weak convergence of an iterative sequence 3. Weak convergence theorem In this section, we obtain the following weak convergence ... 10.1155/FPTA/2006/35390 2 Weak convergence of an iterative sequence monotone and F(T) = VI(C, A), where I is the identit y mapping of H and F(T) is the set of fixed points of T;see[11].InthecaseofC = H = R N , ... Weak convergence of an iterative sequence Theorem 4.1. Let E be a uniformly convex and 2-uniformly smooth Banach space. Let α>0 and let A be an α-inverse strongly accretive operator of E into

Ngày tải lên: 22/06/2014, 22:20

... minimization of DC Functions, Journal of Computational Mathematics, 21, 451-462 (2003) 12. Moudafi, A., Maing´e, P. E.: On the convergence of an approximate proximal method for DC functions, Journal of ... more general class of problems. The results open up the possibility of understanding the convergence of the (DCA) and other algorithms for minimizing differences of convex functions used in numerous applications. Acknowledgment. The ... the convergence analysis of an algorithm for solving optimization problems in which the objective functions can be represented as differences of nonconvex and convex functions. The structure of

Ngày tải lên: 12/10/2015, 16:21

... D such that f is the limit of a sequence {rm }m≥1 of rational functions which converged rapidly to f on D, see the next section for the definition of these types of convergence. Here, we always ... demonstrates a sharp contrast between uniform convergence and rapidly uniform convergence. Indeed, there exists a sequence of polynomials that converges on compact subsets of the unit disk ∆ ⊂ C but is ... the proof of Theorem 4.1 (a) we can find a sequence of positive constants {dk }k≥k0 ↑ ∞ such that for z ∈ B the following estimates hold φmk (z, f (z)) ≤ −dk . Take a sequence {ck }k≥k0 of positive

Ngày tải lên: 16/10/2015, 14:19

... degree of exactness of the the quadrature rule The most common cases are Gauss-Radau quadrature, where one of the nodes is an endpoint of the interval,... extensions of this kind Sequences ... i.e., the computation of the coefficients a j , b j in (4.5.6); (ii) the determination of the zeros of p N (x),and the computation of the associated weights. For the case of the “classical” orthogonal ... own tabulation of weights and abscissas for an unusual choice of W (x). We will therefore give, without any proofs, some useful results that will enable you to do this. Several of the results

Ngày tải lên: 15/12/2013, 04:15

... Instead of building up an approximation to A−1 , it is possible to build up an approximation of A itself Then, instead of calculating the left-hand side of (10.7.4) directly, one solves the set of ... Cholesky decomposition of A is of order N and can be arranged to guarantee that the matrix remains positive definite and nonsingular, even in the presence of finite roundoff This method is due ... x2 + · · · + aiN xN ≤ bi (bi ≥ 0) i = 1, , m1 (10.8.3) m2 of them of the form j = m1 + 1, , m1 + m2 (10.8.4) and m3 of them of the form ak1 x1 + ak2 x2 + · · · + akN xN = bk ≥ k = m1 +

Ngày tải lên: 24/12/2013, 12:16

... configuration space, like the set of possible orders of cities, or the set of possible allocations of silicon “real estate” blocks to circuit elements The number of elements in the configuration ... billions of times the size of an individual atom in all directions This crystal is the state of minimum energy for this system The amazing fact is that, for slowly cooled systems, nature is able to find ... chance, albeit very small, of a system being in a high energy state Therefore, there is a corresponding chance for the system to get out of a local energy minimum in favor of finding a better, more

Ngày tải lên: 24/12/2013, 12:16

... Human Genome Project 24 A CONVERGENCE OF SCIENCE AND LAW DAVID L GOODSTEIN, Ph.D., physics, University of Washington, Vice Provost and Professor of Physics and Applied Physics, ... Law He wrote the amicus briefs on behalf of the National Academy of Engineering in the Kumho case and on behalf of the National Academy of Sciences in the Daubert case These landmark ... 22 Staff of the Science, Technology, and Law Panel, 26 22 1 Introduction This report is a summary of the first meeting of the Science, Technology, and Law Panel of The National

Ngày tải lên: 23/03/2014, 04:20

... A Shamoyan, Characterization of the rate of decrease of the Fourier coefficients of functions of bounded type and of a class of analytic functions with infinitely differentiable ... decrease of the Fourier co- efficients. See for example [H78] for an analysis of support of measures with smooth Cauchy transform. The connection between the smoothness of the boundary value of a function ... Kellay, Boundary behaviour of functions of Nevanlinna class, Indiana Univ Math J 53 (2004), 347–395 [D77] B E J Dahlberg, On the radial boundary values of subharmonic functions, Math Scand

Ngày tải lên: 29/03/2014, 07:20

... 487 presence of a second aB-crystallin gene transcript. Com- plete sequence was derived from expressed sequence tag reads of 30 clones, several of which contained the complete coding sequence, revealing ... unanno- tated genomic sequence from chromosome 21 (BX510931). The ORF encoded a protein sequence of 165 amino acids (Fig. 1; AAZ15808). Sequence com- parisons showed that the predicted protein sequence was ... of cDNAs for members of the a-crystallin family. From a total of about 3700 sequences, 63 correspon- ded to aA-crystallin and 24 to aB-crystallin. However, a third group of 28 clones corresponded

Ngày tải lên: 30/03/2014, 11:20

... of his professional career: “For reasons connected with the imaginary value 6 Of course, in 1919, Lanczos was most certainly not aware of this interpretation, which stems from the discovery of ... apparently un- avoidable divergent nature of the self-energy of a point electron, Lanczos has a stroke of genius: What about displacing the position of the electron off the world-line into complexified ... implications of light-cone related singularities,21 and then only, almost reluctantly, goes to the main topic of the chapter: The derivation of the equations of motions of an electron

Ngày tải lên: 24/04/2014, 16:48

... framework of the much general Banach space? Osilike et al [5] proved the convergence theorems of modified Mann iteration method in the framework of q-uniformly smooth Banach spaces which are also uniformly ... guarantees strong convergence of the modified Mann’s iterative sequence to a fixed point of T in a real Banach spaces with the Fr´chet differentiable e norm We will use the notation: for weak convergence ... Akuchu, BG: Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces Pan Am Math J 12(2), 77–88 (2002) [3] Qihou, L: Convergence theorems of the sequence of iterates for asymptotically

Ngày tải lên: 18/06/2014, 22:20

... set of fixed points of T (s) and by F ix(S) the set of all common fixed points of S, i.e., F ix(S) = s≥0 F ix(T (s)) It is known that F ix(S) is closed and convex ([20], Lemma 1) A mapping A of ... if Tx − Ty ≤ x − y , ∀x, y ∈ H Denote the set of fixed points of the mapping T by F ix(T ) Recall also that a family S := {T (s)}s≥0 of mappings of H into itself is called a nonexpansive semigroup ... Tianjin 300160, People’s Republic of China Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea Department of Information Management, Cheng

Ngày tải lên: 18/06/2014, 22:20

... Mann iteration for the class of continuous and nondecreasing functions. Later in 1991, Borwein and Borwein [6] proved the convergence of the Mann iteration of continuous functions on a bounded closed ... 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 ... solution of (1.2). Question: If g : E → E is continuous but not contraction, what iteration methods can be used for finding a solution of (1.2) (that is a fixed point of g) and how about the rate of convergence

Ngày tải lên: 20/06/2014, 20:20

... method for finding a common element 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 nonexpansive ... 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 ... 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 common

Ngày tải lên: 20/06/2014, 22:20

... subsequences {un} of {xn} Moreover, ωw(xn) consists of exactly one point PROOF Let u Î ωw(xn), then there exists a subsequence {un} of {xn} such that A ({un}) = {u} Since {un} is bounded sequence, ... principle for mappings of asymptotically nonexpansive type in uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity. In 1976, Lim [7] introduce d a concep t of convergence in ... http://www.fixedpointtheoryandapplications.com/content/2011/1/39 Page 3 of 12 Proposition 2.4. Let (X, d, W) be a complete UCW-hyperbolic space with a monotone modulus of uniform convexity. Then the intersection of any decreasing sequence of none- mpty

Ngày tải lên: 21/06/2014, 00:20

... subset Λ of Y con- taining ℜ(z), there exists an o pen neighborhood Π of z such that ℜ(Π) ⊂ Λ.Interms of sequences, ℜ is u.s.c. if for each sequence (z n ) ⊂ X, z n ® z 0 ,andB a cl osed subset of ... p. 812] Let K be a compact subset of the Banach space × and let F be a family of maps of uniformly bounded variation from I into K. Then there exists a sequence of maps ( f n ) n≥1 ⊂ F convergent ... 1 < <τ m = T is any partition of I. The quantity V d X (f , I ) is called the total variation of f. WeshalldenotebyBV(I, X) the space of all functions of bounded variations on I and with

Ngày tải lên: 21/06/2014, 02:20

... Research Article Convergence of Iterative Sequences for Common Zero Points of a Family of m-Accretive Mappings in Banach Spaces Yuan Qing,1 Sun Young Cho,2 and Xiaolong Qin1 Department of Mathematics, ... xn , n ≥ 0, 1.14 where {αn } is a real sequence 0, and Jrn I rA −1 They obtained the strong convergence of the iterative algorithm in the framework of uniformly smooth Banach spaces and reflexive ... the sequence {xn } is bounded Now assume that x∗ is a weak limit point of {xn } and a subsequence {xnj } of {xn } converges weakly to x∗ Then, by Lemma 2.2, we see that x∗ is a fixed point of

Ngày tải lên: 21/06/2014, 05:20

... doi:10.1155/2011/368137 Research Article Convergence of Iterative Sequences for Fixed Point and Variational Inclusion Problems Li Yu and Ma Liang School of Management, University of Shanghai for Science and ... of a strict pseudocontraction and in the zero set of a nonlinear mapping which is the sum of a maximal monotone operator and an inverse strongly monotone mapping Strong convergence theorems of ... identity mapping Recently, many authors considered the convergence of iterative sequences for the variational inequality 1.6 and fixed point problems of nonlinear mappings see, for example, 1–32 In

Ngày tải lên: 21/06/2014, 05:20

... solution of VI 1.12 ; hence, x ∈ Ω x∗ , the unique solution of VI 3.4 As a matter of fact, we We further prove that x have by 3.36 xtn − x ≤ f x − x , xtn − x , 1−ρ x ∈ Ω 3.43 Therefore, the weak convergence ... By uniqueness, we have x guarantee that xt → x∗ in norm, as t → The proof is complete Proof By Conclusions 1–4, the proof of Theorem 3.1 is completed 3.44 x∗ This is sufficient to 14 Fixed Point ... solutions of equilibrium problems and zeros of maximal monotone operators,” Journal of Optimization Theory and Applications, vol 142, no 3, pp 431–449, 2009 23 Y Yao, Y.-C Liou, and J.-C Yao, “Convergence

Ngày tải lên: 21/06/2014, 07:20