... the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings ... interleaving of theory and applications and their creative symbiotic evolution is axiomatic Harmonic analysis is a wellspring of ideas and applicability that has flourished, developed, and deepened over ... development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences Historically, Fourier...
... retraction P of C onto D We know that if E is smooth and P is a retraction of C onto D, then P is sunny and nonexpansive if and only if for each x ∈ C and z ∈ D, x − Px,J(z − Px) ≤ (2.4) For more details, ... implies that z ∈ F(Jr ) = A−1 Let {Jtn x} and {Jsn x} be subsequences of {Jt x} such that {Jtn x} and {Jsn x} converge strongly to y and z as tn → ∞ and sn → ∞, respectively From z ∈ A−1 0, we ... [25] H Miyake and W Takahashi 95 Let D be a subset of C and let P be a retraction of C onto D, that is, Px = x for each x ∈ D Then P is said to be sunny [16] if for each x ∈ C and t ≥ with Px...
... paper size and orientation, as well as margins In Excel 97 and later versions, browse in Tools ⇒ Customize to see (and select) your Toolbars and their Commands You can click on a command and then ... curve, right-click, and select Format Data Series Then for the Line pick the Style, Color, and Weight you like, and for Marker the Style, Forground and Background color, and Size And so it goes: ... or the cell handle; if nothing is specified, go to the center of the cell and use its standard pointer, the hollow cross 1.3 A simple spreadsheet and graph 1.3 A simple spreadsheet and graph The...
... Byszewski and Lakshmikantham [7] proved the existence and uniqueness of mild solutions for nonlocal semilinear differential equations when f and g satisfy Lipschitz type conditions In [8], Ntouyas and ... Byszewski and Akca [9] established the existence of solution to functional-differential equation when the semigroup is compact, and g is convex and compact on a given ball Subsequently, Benchohra and ... of g is compact, Lipschitz, and g is not compact and not Lipschitz, respectively The goal of this article is to make use of the Hausdorff measure of noncompactness and the fixed point theory to...
... 1.2 [19] Let C be a compact convex subset of a Banach space E and let S and T be nonexpansive mappings on C with ST = TS Let x1 ∈ C and define a sequence {xn } in C by n xn+1 = n αn Si T j xn + ... with Krasnosel’ski˘ and Mann’s type sequences [14, 16] This is a generalization of [19, Lemma 1] ı See also [8, 20] Lemma 2.1 Let {zn } and {wn } be sequences in a Banach space E and let {αn } be ... )/2 We note that < a < Fix k, ∈ N and ε > Then there exists m ≥ such that a ≤ − αn , wn+1 − wn − zn+1 − zn ≤ ε, and wn+ j − zn+ j − wn − zn ≤ ε/2 for all n ≥ m and j = 1,2, ,k In the case of d...
... University (Project No R2553C222), and the Commission on Higher Education and the Thailand Research Fund (Project No MRG5380247) Cho and Petrot Journal of Inequalities and Applications 2011, 2011:21 ... convex subset of a Hilbert space H and g: H ® H be a mapping such that K ⊂ g(H) Let A: H ® H be a hemicontinuous on K and g- Cho and Petrot Journal of Inequalities and Applications 2011, 2011:21 ... reduces to a result presented by Kim and Buong [9] Cho and Petrot Journal of Inequalities and Applications 2011, 2011:21 http://www.journalofinequalitiesandapplications.com/content/2011/1/21...
... called the K-mapping generated by T1 , , TN and γn,1 , γn,2 , , γn,N In this paper, motivated by Kim and Xu , Marino and Xu 10 , Xu , Yao et al , andShang et al , we introduce a composite iterative ... Takahashi and K Shimoji, “Convergence theorems for nonexpansive mappings and feasibility problems,” Mathematical and Computer Modelling, vol 32, no 11–13, pp 1463–1471, 2000 M Shang, Y Su, and X ... } and {zn } be bounded sequences in a Banach space X, and let {βn } be a sequence in 0, with < lim infn → ∞ βn ≤ lim supn → ∞ βn < Suppose that xn βn xn 1 − βn zn 1.12 for all integer n ≥ 0, and...
... har poonupw, and (A4), we have B(u,w) ≤ for all u ∈ C For t with < t ≤ and u ∈ C, let ut = tu + (1 − t)w Since u ∈ C and w ∈ C, we have ut ∈ C and hence B(ut ,w) ≤ So, from (A1) and (A4), we ... and Optimization and Their Applications (Haifa, 2000), D Butnariu, Y Censor, and S Reich, Eds., vol of Studies in Computational Mathematics, pp 473–504, North-Holland, Amsterdam, The Netherlands, ... f (x) for x ∈ H) In this paper, motivated by Combettes and Hirstoaga [1], Moudafi [9], S Takahashi and W Takahashi [3], Marino and Xu [8], and Wittmann [10], we introduce a general iterative scheme...
... ρn < n→∞ n→∞ Wang and Wang Journal of Inequalities and Applications 2011, 2011:41 http://www.journalofinequalitiesandapplications.com/content/2011/1/41 Page of Assume that (xn) and (yn) are bounded ... knowledge that ||en||® and λn 2λn = → 0, ρn 2λn + δn δn δn = → 1, 2ρn 2λn + δn Wang and Wang Journal of Inequalities and Applications 2011, 2011:41 http://www.journalofinequalitiesandapplications.com/content/2011/1/41 ... article as: Wang and Wang: On relaxed and contraction-proximal point algorithms in hilbert spaces Journal of Inequalities and Applications 2011 2011:41 Submit your manuscript to a journal and benefit...
... problems is more general and has had a great impact and influence in the development of several branches of pure, applied, and engineering sciences For more information and results on the general ... monotone and Lipschitz continuous mapping with a constant τA and B : H ® CB(H) be νB-strongly monotone and Lipschitz continuous mapping with a constant τB Let g : H ® H be νg-strongly monotone and ... monotone and Lipschitz continuous mapping with a constant τA , and B : K ® CB(H) be νB-strongly monotone and Lipschitz continuous mapping with a constant τB Let g : K ® K be a νg-strongly monotone and...
... Feasibility and Optimization and Their Applications (Haifa, 2000), D Butnariu, Y Censor, and S Reich, Eds., vol of Stud Comput Math., pp 473–504, North-Holland, Amsterdam, The Netherlands, 2001 ... 3.22 Journal of Inequalities and Applications and hence ≤ φ zt , y From A3 , we have ≤ φ q, y for all y ∈ C and hence q ∈ EP φ Therefore, q ∈ F S ∩ EP φ On the other hand, we note that xn − q ... E Blum and W Oettli, “From optimization and variational inequalities to equilibrium problems,” The Mathematics Student, vol 63, no 1–4, pp 123–145, 1994 A Moudafi and M Th´ ra, “Proximal and dynamical...
... 3.1 and 3.2 improve and generalize Theorem 3.1 of from contractive mapping to φ-strongly pseudocontractive mapping and pseudocontractive mapping, respectively Theorems 3.1 and 3.2 also improve and ... by Theorems 3.6 and 3.8 So, Theorems 3.6 and 3.8 generalize Theorem 3.6 of Acknowledgments The authors are grateful to Professor J C Yao and the referees for valuable comments and suggestions ... Theory and Applications Preliminaries A mapping T with domain D T and range R T in H is said to be demiclosed at a point p ∈ H if {xn } is a sequence in D T which converges weakly to x ∈ D T and...
... 1.16 ∀n ≥ 1, and proved that, under certain appropriate conditions over n and rn , the sequences {xn } and {un } both converge strongly to z PF T ∩EP G f z By combing the schemes 1.7 and 1.16 , ... different with ones of others in the literatures and our result extends and improves the ones of Colao et al and some others 6 Fixed Point Theory and Applications Preliminaries Let C be a closed ... mappings and equilibrium problems,” Journal of Nonlinear and Convex Analysis, vol 9, no 1, pp 37–43, 2008 15 S Plubtieng and R Punpaeng, “A new iterative method for equilibrium problems and fixed...
... β n / γ n for every n ∈ N Pn and let S : X → Y be Let P , Q : Y → Y be given by P Pn and Q S S, S, Recall that we will write S instead of S By a , b , and c and since xn is equilateral we ... 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 ... II X is reflexive and has property WORTH, or III X has both the properties WORTH and WABS, then X has the property AMC and thus the wFPP It is known that reflexivity implies WABS, and thus II implies...
... [8–10], Huang and Aslam Noor [6], and some others Let H be a real Hilbert space whose inner product and norm are denoted by ·, · and · , respectively Let C be a closed convex subset of H and let T ... (iii) v1 > u1 μ2 , v2 > u2 μ2 and v3 > u3 μ2 , then the sequences {xn }, { yn }, and {zn } converge strongly to x∗ , y ∗ , and z∗ , respectively Proof Since x∗ , y ∗ , and z∗ are the common elements ... v2 > u2 μ2 and v3 > u3 μ2 , then the sequences {xn }, { yn }, and {zn } converge strongly to x∗ , y ∗ , and z∗ , respectively Remark 3.4 Theorem 3.3 includes Theorem 3.5 of Huang and Aslam Noor...
... following theorem: Theorem 2.5 Let C1 and C2 be two nonempty, closed and convex subsets in a real Hilbert space H and let T1 and T2 be two nonexpansive mappings on C1 and C2 , respectively, such that ... Hilbert space H and let T : C → H be a nonexpansive mapping such that F (T ) = ∅ Assume that {αn } and {βn } are sequences in [0,1] such that αn → and βn → Then, the sequences {xn }, {yn } and {zn } ... 0, and limn (tn+1 − tn ) = and they proved that {xn } converges strongly to u0 = PF x0 Recently, Nguyen Buong, introduced a new approach in order to replace closed and convex subsets Cn and...
... opportunities and challenges posed by converged networks Describe the characteristics of network architectures: fault tolerance, scalability, quality of service and security Install and use IRC clients and ... businesses, to address emergencies, to inform individuals, and to support education, science, and government Play video to watch how the Internet, and its underlying technology, brings opportunities ... We Learn • • • • Communication, collaboration, and engagement are fundamental building blocks of education Robust and reliable networks support and enrich student learning experiences Courses...
... of standards that are common to the C# community and broad in scope: code, design, and design pattern standards Code and design standards are presented from two perspectives: pure (policy) and ... attention, and it’s your choice whether you use them Generally, there are two categories of standards: internal and external Internal standards are those standards that are in-house standards, ... Process), and (3) a set of supplementary policies The Standard: Code Management The standard acknowledges that code is a valuable resource that benefits from management throughout its development and...