l2 0 1 and in general hilbert spaces

... 19 5 19 6 2 10 212 216 2 20 224 227 2 31 237 2 40 10 Gabor Frames in (Z) 10 . 1 Translation and modulation on (Z) 10 . 2 Gabor systems in (Z) through sampling 10 . 3 Shift-invariant systems ... frame is {S 1 fk }3 k =1 = {S 1 e1 , S 1 e1 − S 1 e2 , S 1 e1 + S 1 e2 } 1 1 = { e1 , e1 − e2 , e1 + e2 } 3 Frames in Finite-dimensional Inner Product Spaces Via Theorem 1. 1.5, the representation ... Continuous frames 5.9 Frames and signal processing 5. 10 Exercises 97 98 10 5 10 8 11 2 11 6 12 1 12 6 12 9 1 30 13 3...

Ngày tải lên: 27/06/2014, 05:20

... [9] [ 10 ] [11 ] [12 ] [13 ] [14 ] [15 ] [16 ] [17 ] [18 ] [19 ] S Atsushiba and W Takahashi, Approximating common fixed points of two nonexpansive mappings in Banach spaces, Bull Austral Math Soc 57 (19 98), ... Banach spaces, Kodai Math J 14 (19 91) , no 3, 358–365 S Kamimura and W Takahashi, Approximating solutions of maximal monotone operators in Hilbert spaces, J Approx Theory 10 6 ( 200 0), no 2, 226–2 40 ... Science Publishers, New York, 200 2, pp 15 – 31 R E Bruck and S Reich, A general convergence principle in nonlinear functional analysis, Nonlinear Anal (19 80) , no 5, 939–9 50 R E Bruck Jr., A strongly...

Ngày tải lên: 23/06/2014, 00:20

... a sine and cosine wave, including the 1. 5 More on graphs 10 11 12 13 14 15 16 17 18 19 C second sine 0 0. 707 10 6 78 0. 13 656323 0. 2678784 0. 707 10 6 78 0. 38889 916 1. 2251E -16 0. 49497475 -0. 707 10 6 8 0. 58 202 873 ... -4. 9 01 E -16 8.576E -17 0. 707 10 6 78 -0. 13 65632 -0. 2678784 0. 707 10 6 78 -0. 3888992 D 1. 5 0. 5 -0. 5 -1 -1. 5 E F sine wave sine B sine 40 80 angle second sine wave 0. 5 sine A x 10 11 12 13 14 15 16 17 18 19 ... -0. 707 10 6 8 0. 58 202 873 - 0. 646 715 67 -0. 707 10 6 8 0. 6865497 0. 7 -2.45E -16 0. 707 10 6 78 0. 6865497 0. 646 715 67 0. 707 10 6 78 0. 58 202 873 3.6754E -16 0. 49497475 -0. 707 10 6 8 0. 38889 916 -1 0. 2678784 -0. 707 10 6 8 0. 13 656323...

Ngày tải lên: 17/03/2014, 02:20

... Province (BK 2 01 0 309 and BK 200 917 9), the Natural Science Foundation of Jiangsu Education Committee (10 KJB1 10 0 12 and 09 KJB1 10 0 10 ) , the Yangzhou University Scholarship for Overseas Studies and the ... University ( 2 01 0CXJ 003 and 2 01 1CXJ 002 ) References [1] Ahmed, NU: Optimal feedback control for impulsive systems on the space of finitely additive measures Publ Math Debrecen 70, 3 71 393 ( 200 7) 18 [2] ... compactness in Banach spaces Anal Appl 8, 211 –225 ( 2 01 0) [14 ] Xue, XM: Nonlocal nonlinear differential equations with a measure of noncompactness in Banach spaces Nonlinear Anal TMA 70, 2593–2 6 01 ( 200 9)...

Ngày tải lên: 21/06/2014, 17:20

... S1 S1 S2 S1 S3 S2 S1 x5 , x7 = S4 S3 S2 S1 S1 S1 S1 S1 S1 S2 S1 S1 S1 S1 S1 S2 S1 S1 S1 S1 S2 S1 S1 S1 S2 S1 S1 S2 S1 S3 S2 S1 S1 S1 S1 S1 S2 S1 S1 S1 S1 S2 S1 S1 S1 S2 S1 S1 S2 S1 S3 S2 S1 S1 ... S1 S2 S1 S3 S2 S1 S1 S2 S1 S3 S2 S1 x4 , x6 = S4 S3 S2 S1 S1 S1 S1 S1 S2 S1 S1 S1 S1 S2 S1 S1 S1 S2 S1 S1 S2 S1 S3 S2 S1 S1 S1 S1 S2 S1 S1 S1 S2 S1 S1 S2 S1 S3 S2 S1 (1. 3) S1 S1 S2 S1 S1 S2 S1 ... S1 x1 , x3 = S4 S3 S2 S1 S1 S2 S1 S3 S2 S1 x2 , x4 = S4 S3 S2 S1 S1 S1 S2 S1 S1 S2 S1 S3 S2 S1 S1 S2 S1 S3 S2 S1 x3 , x5 = S4 S3 S2 S1 S1 S1 S1 S2 S1 S1 S1 S2 S1 S1 S2 S1 S3 S2 S1 S1 S1 S2 S1...

Ngày tải lên: 23/06/2014, 00:20

... Math Stud 63, 12 3 14 5 (19 94) 12 Xu, HK: Iterative algorithms for nonlinear operators J Lond Math Soc 66 (1) , 2 40 256 ( 200 2) doi: 10 . 11 12/ S 002 46 10 7 0 200 3332 doi: 10 . 11 86/ 10 2 9-242X- 2 01 1- 21 Cite this ... mappings Nonlinear Anal 61, 3 41 3 50 ( 200 5) doi: 10 . 10 1 6/j.na. 200 3 .07 .02 3 Noor, MA: General variational inequalities and nonexpansive mappings J Math Anal Appl 3 31, 8 10 822 ( 200 7) doi: 10 . 10 1 6/j.jmaa. 200 6 .09 .03 9 ... doi: 10 . 10 1 6/j.jmaa. 200 6 .09 .03 9 Noor, MA, Huang, Z: Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings Appl Math Comput 19 1, 504 –5 10 ( 200 7) doi: 10 . 10 1 6/j.amc. 200 7 .02 .11 7 Qin,...

Ngày tải lên: 21/06/2014, 01:20

... Kn 1 xn 1 |αn − αn 1 | Ayn 1 βn 1 − βn Kn 1 xn 1 βn 1 − βn Kn 1 xn 1 γααn xn − xn 1 L βn 1 − βn xn − xn 1 γ|αn − αn 1 | f xn 1 M |αn − αn 1 | γn,j − γn 1, j , j 2.7 where L sup{ xn 1 Kn 1 xn 1 : n ... 4448–44 60, 200 9 10 G Marino and H.-K Xu, “A general iterative method for nonexpansive mappings in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol 318 , no 1, pp 43–52, 200 6 11 ... αn 1 f xn 1 xn − xn 1 βn − βn 1 xn 1 − βn Kn xn 1 − Kn 1 xn 1 |αn − αn 1 | Ayn 1 ≤ − αn γ xn − xn 1 γααn xn − xn 1 − γ − γα αn N − βn M γ|αn − αn 1 | f xn 1 βn − βn 1 xn 1 − βn Kn xn 1 − Kn−1...

Ngày tải lên: 21/06/2014, 11:20

... China under Grant no 10 7 7 10 5 0 References [1] P L Combettes and S A Hirstoaga, “Equilibrium programming in Hilbert spaces, ” Journal of Nonlinear and Convex Analysis, vol 6, no 1, pp 11 7 13 6, 200 5 ... xn +1 ≤ − αn +1 γ yn +1 − yn + αn +1 − αn + γ αn +1 α xn +1 − xn + αn +1 − αn ASyn f xn (3 .12 ) Substitute (3 .11 ) into (3 .12 ) yields that xn+2 − xn +1 ≤ − (γ − γα)αn +1 xn +1 − xn + M2 αn +1 − αn + rn +1 ... that yn +1 − yn ≤ yn +1 − yn xn +1 − xn + − rn rn +1 yn +1 − xn +1 (3. 10 ) It follows that yn +1 − yn ≤ xn +1 − xn + M1 rn +1 − rn , (3 .11 ) where M1 is an appropriate constant such that M1 ≥ sup n 1 yn −...

Ngày tải lên: 21/06/2014, 22:20

... proximal point algorithm J Global Optim 50, 5 31 535 ( 2 01 1) doi: 10 . 10 0 7/s 10 8 9 8 01 0-9 611 -z doi: 10 . 11 86/ 10 2 9-242X- 2 01 1- 41 Cite this article as: Wang and Wang: On relaxed and contraction-proximal point algorithms ... Soc 13 5, 99– 10 6 ( 200 7) 11 Tan, KK, Xu, HK: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process J Math Anal Appl 17 8, 3 01 – 308 (19 93) doi: 10 . 10 0 6/jmaa .19 93 .1 309 12 ... iterations in a Hilbert space Math Programming Ser 87, 18 9– 202 ( 200 0) Xu, HK: Iterative algorithms for nonlinear operators J Lond Math Soc 66, 2 40 256 ( 200 2) doi: 10 . 11 12/ S 002 46 10 7 0 200 3332 Goebel,...

Ngày tải lên: 21/06/2014, 00:20

... doi: 10 . 10 1 6 /08 93-9659(88) 900 54-7 Noor, MA: Some developments in general variational inequalities Appl Math Comput 15 2, 19 9–277 ( 200 4) doi: 10 . 10 1 6/ S 009 6- 300 3 (03 )00 558-7 Noor, MA: Variational Inequalities ... 1, 75–86 ( 200 8) 10 Noor, MA: Differentiable nonconvex functions and general variational inequalities Appl Math Comput 19 9, 623–6 30 ( 200 8) doi: 10 . 10 1 6/j.amc. 200 7. 10 . 023 11 Noor, MA: Extended general ... approximation-solvability of nonlinear variational inequalities Comput Math Appl 41, 505 – 512 ( 200 1) doi: 10 . 10 1 6/S0898 -12 21 (00 )00 292-3 16 Verma, RU: Generalized system for relaxed variational inequalities and its projection...

Ngày tải lên: 21/06/2014, 01:20

... un 1 − Sn 1 un 1 βn un 1 − βn Sun 1 − βn 1 un 1 − βn 1 Sun 1 ≤ βn − βn 1 un 1 − Sun 1 3.49 From 3.48 , 3.49 , and 3.42 , we obtain that yn − yn 1 ≤ xn − xn 1 M0 |λn − λn 1 | a βn − βn 1 un 1 ... Sun 1 ≤ xn − xn 1 |λn − λn 1 |M1 βn − βn 1 M1 , 3. 50 12 Journal of Inequalities and Applications where M1 is an appropriate constant such that M0 a M1 ≥ un 1 − Sun 1 , ∀n ∈ N 3. 51 From 3. 41 and ... un − Sn 1 un 1 ≤ Sn un − Sn un 1 ≤ un − un 1 Sn un 1 − Sn 1 un 1 Sn un 1 − Sn 1 un 1 3.42 Journal of Inequalities and Applications From un Tλn xn 1 and un λn y − un , un 1 − xn ≥ 0, 1 y − un...

Ngày tải lên: 21/06/2014, 05:20

... vol 70, no 9, pp 306 5– 307 1, 200 9 G Marino and H.-K Xu, “A general iterative method for nonexpansive mappings in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol 318 , no 1, ... and the referees for valuable comments and suggestions This work was supported by The Key Program of NSFC Grant no 708 3 10 0 5 , the National Natural Science Foundation of China 10 6 711 35, 1 10 2 606 3 ... Nonlinear Analysis: Theory, Methods & Applications, vol 61, no 6, pp 10 3 1 10 3 9, 200 5 10 T Shimizu and W Takahashi, “Strong convergence to common fixed points of families of nonexpansive mappings,”...

Ngày tải lên: 21/06/2014, 07:20

... xn 1 δn − δn 1 Bxn 1 δn 1 BWn 1 zn 1 − δn BWn zn 1 nγ δn B xn − xn 1 Wn zn − Wn zn 1 f xn − f xn 1 n xn 1 xn 1 − δn 1 Bxn 1 − I − δn 1 B − n 1 γf nγ nA n γf − n AWn 1 zn 1 n 1 A nA δn − δn 1 Bxn 1 ... Bxn 1 Wn zn 1 Wn 1 zn 1 I − δn B − nA Wn zn − Wn zn 1 Wn zn 1 − Wn 1 zn 1 n 1 AWn 1 zn 1 δn B xn − xn 1 δn Bxn 1 − I − δn B − n AWn zn 1 nA Wn zn − Wn zn 1 Wn zn 1 − Wn 1 zn 1 δn B Wn 1 zn 1 − ... BWn 1 zn 1 | ≤ n 1 n γκ − n| − δn β − | n − n 1 |γ n 1 − n| zn − zn 1 Wn zn 1 − Wn 1 zn 1 A Wn 1 zn 1 − Wn zn 1 n δn B xn − xn 1 xn − xn 1 nγ n 2|δn 1 − δn |M2 Wn zn 1 − Wn 1 zn 1 δn B Wn 1 zn−1...

Ngày tải lên: 21/06/2014, 11:20

... 3.8 and 3.9 , and 3.5 we obtain Sw Sxβ Sxγ ≤ δ P Q Sw δ u 3. 10 ≤ δ xβ xδ δ Hence w ≤ δ 2 Finally, from 3.7 and 3 .11 we have w − 1/ 2 ≤ w ≤ Therefore, if δ < AMC property √ δ2 3δ δ δ 3 .11 δ /2 and ... QSxβ 0, P Sxγ δ and Sxβ − Sxγ ≤ δ, Sxγ , 0, for all y ∈ Y , P y Qy Therefore, since en is 1- unconditional Sxβ Sxγ QSxβ P Sxγ QSxβ − P Sxγ Sxβ − Sxγ ≤ δ 3 .1 Fixed Point Theory and Applications S 1 ... Bulletin of the Australian Mathematical Society, vol 67, no 2, pp 17 7 18 5, 200 3 S R Cowell and N J Kalton, “Asymptotic unconditionality,” http://arxiv.org/abs /08 09.2294 J Garc´a-Falset and E...

Ngày tải lên: 21/06/2014, 20:20

... projection methods in the context of the approximation solvability of the SNVID problems (1. 7)– (1. 9), (1. 13)– (1. 15), and SNVI problems (1. 16)– (1. 18) Algorithm 2 .1 For any x0 , y0 ,z0 ∈ C, compute ... (3 .11 ) into (3. 10 ) , we obtain zn +1 − z∗ ≤ θ3 xn +1 − x∗ , (3 .12 ) zn − z∗ ≤ θ3 xn − x∗ (3 .13 ) which implies Similarly, substituting (3 .13 ) into (3.9) yields that xn +1 − x∗ ≤ − αn xn − x∗ + αn 1 ... Theory and Applications, vol 12 1, no 1, pp 203 –2 10 , 200 4 [9] R U Verma, “Generalized class of partially relaxed monotonicities and its connections,” Advances in Nonlinear Variational Inequalities,...

Ngày tải lên: 22/06/2014, 18:20

Ngày tải lên: 05/08/2014, 09:46

... ) u0 = 0. 000 000 000 000 00 1. 98294 5 01 7736 413 −2 .00 000 000 000 000 u1 = 0. 0 500 000 000 000 0 1. 832285258 509 282 1. 8 500 000 000 000 0 u 20 = 1 .00 000 000 000 000 0 0. 84 907 0438 504 779 1 .00 000 000 000 000 0 Example ... 1. 666694444 908 047 u1 = 0. 0 500 000 000 000 00 1. 5 409 06 200 737 406 u 20 = 1 .00 000 000 000 000 0 0. 84 907 0438 504 779 Exact Solution p∗ (ui ) −2 .00 000 000 000 000 0 1. 8 500 000 000 000 00 1 .00 000 000 000 000 0 Next, we ... following table: 13 Table 2.2 Iteration ui App Solution X(ui ) Exact Solution p∗ (ui ) u0 = 0. 000 000 000 000 00 1. 99999 809 26 513 67 −2 .00 000 000 000 000 u1 = 0. 0 500 000 000 000 0 1. 84844 706 2448525 1. 8 500 000 000 000 0...

Ngày tải lên: 25/08/2015, 14:54

... Website: www.bkacad.com Networking Career Opportunities • Information Technology and networking careers are growing and evolving as fast as the underlying technologies and services H c vi n m ng ... Online learning opportunities can decrease time-consuming and costly travel yet still ensure that all employees are adequately trained to perform their jobs in a safe and productive manner Online ... courseware and delivery offer many benefits to businesses such as: – Current and accurate training materials – Availability of training to a wide audience – Consistent quality of instruction...

Ngày tải lên: 12/12/2013, 14:15

... 5 60- 2 fm.qxd 10 / 27 /05 4: 30 PM Page i Pro NET 2 .0 Code and Design Standards in C# Mark Horner 5 60- 2 fm.qxd 10 / 27 /05 4: 30 PM Page ii Pro NET 2 .0 Code and Design Standards in C# Copyright © 200 6 ... Springer-Verlag New York, Inc., 233 Spring Street, 6th Floor, New York, NY 10 0 13 Phone 1- 800 -SPRINGER, fax 2 01 -348-4 505 , e-mail orders-ny@springer-sbm.com, or visit http://www.springeronline.com ... Standard: Unit Testing The standard acknowledges the importance of unit testing, which is used to examine the reliability of calling the methods of an object 11 5 60- 2 ch 01. qxd 12 10 / 27 /05 4 :15 ...

Ngày tải lên: 14/02/2014, 10:20