fixed footplate and malleus closed cavity

Ngày tải lên: 13/12/2013, 05:15

... when n = 2; it has been proved for n = by Davenport and Heilbronn [7] in case K = Q, and by Datskovsky and Wright in general [6]; and for n = 4, and K = Q by Bhargava [3], [2] A weaker version of ... unless either |H| = 2, or |Q| = |H| and |H| = 3, In case |Q| = 2, |H| = 4, the group G is nilpotent and Proposition 2.8 is proved by Kl¨ners and Malle u On the other hand, NK (X 1/|H| , Q)X p/(p−1)|G| ... fixed degree and bounded discriminant By Jordan S Ellenberg and Akshay Venkatesh* Abstract We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant...

Ngày tải lên: 06/03/2014, 08:21

... ) is closed and convex under the assumptions of Theorem 3.2 A mapping T : C → X is said to be quasi-nonexpansive with respect to Df if F (T ) = ∅ and Df (v, T x) ≤ Df (v, x) for all x ∈ C and ... Int(D), and let C ⊆ Int(D) a be a nonempty closed convex subset of X If T : C → C is quasi-nonexpansive with respect to Df , then F (T ) is a closed convex subset Proof Let x ∈ F (T ) and choose ... convergence and strong convergence of a sequence {xn } to v in a Banach space by xn v and xn → v, respectively For a nonempty closed convex subset C of a Banach space X, a mapping T : C → X is demiclosed...

Ngày tải lên: 18/06/2014, 22:20

... ) is closed and convex under the assumptions of Theorem 3.2 A mapping T : C → X is said to be quasi-nonexpansive with respect to Df if F (T ) = ∅ and Df (v, T x) ≤ Df (v, x) for all x ∈ C and ... Int(D), and let C ⊆ Int(D) a be a nonempty closed convex subset of X If T : C → C is quasi-nonexpansive with respect to Df , then F (T ) is a closed convex subset Proof Let x ∈ F (T ) and choose ... convergence and strong convergence of a sequence {xn } to v in a Banach space by xn v and xn → v, respectively For a nonempty closed convex subset C of a Banach space X, a mapping T : C → X is demiclosed...

Ngày tải lên: 20/06/2014, 04:20

... generalize and strengthen Theorem 1.2 and the results due to Dotson [15], Jungck and Sessa [16], Lami Dozo [17] and Latif and Tweddle [18] We also extend and unify well-known results on fixed points and ... [1] and Pant [2], respectively A point x in M is said to be a common fixed point (coincidence point) of f and T if x = fx Î Tx (fx Î Tx) We denote by F(f) and F(T) the set of fixed points of f and ... or X is an Opial’s space Then, f and T have a common fixed point Page of Al-Mezel Fixed Point Theory and Applications 2011, 2011:99 http://www.fixedpointtheoryandapplications.com/content/2011/1/99...

Ngày tải lên: 20/06/2014, 21:20

... generalize and strengthen Theorem 1.2 and the results due to Dotson [15], Jungck and Sessa [16], Lami Dozo [17] and Latif and Tweddle [18] We also extend and unify well-known results on fixed points and ... [1] and Pant [2], respectively A point x in M is said to be a common fixed point (coincidence point) of f and T if x = fx Î Tx (fx Î Tx) We denote by F(f) and F(T) the set of fixed points of f and ... or X is an Opial’s space Then, f and T have a common fixed point Page of Al-Mezel Fixed Point Theory and Applications 2011, 2011:99 http://www.fixedpointtheoryandapplications.com/content/2011/1/99...

Ngày tải lên: 20/06/2014, 21:20

... al Fixed Point Theory and Applications 2011, 2011:25 http://www.fixedpointtheoryandapplications.com/content/2011/1/25 Page 11 of 14 and S is an affine mapping If cl(Y - {q}) is compact and S and ... ordered metric space and T, f, and g be selfmaps on Y Suppose that T is continuous, cl(T(Y )) is compact and f and g are affine and continuous and T(Y ) ⊂ f(Y ) ∩g(Y ) Let (T, f) and (T, g) be partially ... space X, T, f, and g be selfmaps on X such that u is common fixed point of f, g, and T and T (∂M ∩ M) ⊂ M Suppose that f and g are continuous and affine on PM (u), q Î Fix(f ) ∩ Fix(g), and PM (u)...

Ngày tải lên: 21/06/2014, 01:20

... in C with xn then x ∈ F S x and xn − Sxn → 0, Fixed Point Theory and Applications Lemma 1.4 see 28 Let {xn } and {yn } be bounded sequences in a Hilbert space H, and let {βn } be a sequence ... and Jsn I sn W −1 , {rn } is a sequence where u ∈ C is a fixed element, Jrn in 0, 2α , {sn } is a sequence in 0, 2β and {αn }, {βn }, {γn }, and {δn } are sequences in 0, Fixed Point Theory and ... | < ∞, ∞ n |λn − λn | < ∞, 1.8 Fixed Point Theory and Applications In 2007, Y Yao and J.-C Yao 31 further obtained the following theorem Theorem YY Let C be a closed convex subset of a real Hilbert...

Ngày tải lên: 21/06/2014, 05:20

... 2 Fixed Point Theory and Applications We present new definitions of asymptotic center and asymptotic radius that is for a mapping and obtain new results Definition 1.1 Let C be a bounded closed ... S C Bose and S K Laskar, Fixed point theorems for certain class of mappings,” Journal of Mathematical and Physical Sciences, vol 19, no 6, pp 503–509, 1985 D Downing and W A Kirk, Fixed point ... semicontinuous and S z for every z ∈ Za C, {xn } is a compact convex set we can apply the Kakutani-Bohnenblust-Karlin Theorem in to obtain a fixed point for S z and hence for T Fixed Point Theory and Applications...

Ngày tải lên: 21/06/2014, 11:20

... stable if and only if 1.3 is iii t a h s ds −→ ∞, as t −→ ∞ 1.9 Fixed Point Theory and Applications Theorem 1.3 Burton Suppose that r t r, a constant Let f be odd, increasing on 0, L , and satisfies ... comparison,” Fixed Point Theory, vol 4, no 1, pp 15–32, 2003 B Zhang, Fixed points and stability in differential equations with variable delays,” Nonlinear Analysis: Theory, Methods and Applications, ... 2 Fixed Point Theory and Applications Many authors have investigated the special cases of 1.1 and 1.2 Since Burton used fixed point theory to investigate...

Ngày tải lên: 21/06/2014, 11:20

... Burton, Fixed points and stability of a nonconvolution equation,” Proceedings of the American Mathematical Society, vol 132, no 12, pp 3679–3687, 2004 T A Burton and T Furumochi, Fixed points and ... t , and c2 t e t Thus, we know that 2.7 includes 2.1 , 2.3 , and 2.5 as special cases Our aim here is to generalize Theorems B and C to 2.7 Theorem 2.1 Suppose that τj is differential, and there ... s bj s − qj s H s ds n cj s ds ≤ α2 ε < j 2.19 Fixed Point Theory and Applications For any x, y ∈ S, it follows from 2.13 , conditions i and ii , and Doob’s Lp -inequality see 10 that px s − py...

Ngày tải lên: 21/06/2014, 23:20

... space E, τ and let T, f, and g be selfmaps of M Suppose that f and g are affine and nonexpansive with q ∈ F f ∩ F g , and T M ⊂ f M ∩ g M If the pairs {T, f} and Fixed Point Theory and Applications ... Hussain and Jungck , Hussain and Khan , Hussain and Rhoades , Jungck and Sessa 13 , Khan and Akbar 19, 20 , Pathak and Hussain 21 , Sahab et al 12 , Sahney et al 26 , Singh 11, 27 , Tarafdar , and ... space E, τ and let T, f, and g be selfmaps of M Suppose that f and g are affine and nonexpansive with q ∈ F f ∩ F g , and T M ⊂ f M ∩ g M If the pairs {T, f} and {T, g} are subcompatible and T is...

Ngày tải lên: 22/06/2014, 11:20

... 14 Fixed Point Theory and Applications 22 J M Rassias, “Solution of a problem of Ulam,” Journal of Approximation Theory, vol 57, no 3, pp 268–273, 1989 23 L C˘ dariu and V Radu, Fixed points and ... to the proofs of Theorems 2.3 and 4.2 Choonkil Park 11 Corollary 4.5 Let r > and θ be nonnegative real numbers, and let f : A → B be a mapping satisfying 2.25 and 4.5 Then there exists a unique ... is similar to the proofs of Theorems 2.3 and 5.2 Corollary 5.5 Let r > and θ be nonnegative real numbers, and let f : A → A be a mapping satisfying 3.7 and 5.5 Then there exists a unique Lie...

Ngày tải lên: 22/06/2014, 11:20

... 2r −1 and we get the desired result (3.23) 12 Fixed Point Theory and Applications Theorem 3.4 Let f : A → A be a mapping for which there exists a function ϕ : A3 → [0, ∞) satisfying (3.3) and (3.4) ... no 1, pp 126–130, 1982 [21] L C˘ dariu and V Radu, Fixed points and the stability of Jensen’s functional equation,” Journal a of Inequalities in Pure and Applied Mathematics, vol 4, no 1, article ... → A} (3.6) and introduce the generalized metric on X: d(g,h) = inf C ∈ R+ : g(x) − h(x) It is easy to show that (X,d) is complete A ≤ Cϕ(x,x,x), ∀x ∈ A (3.7) 10 Fixed Point Theory and Applications...

Ngày tải lên: 22/06/2014, 19:20

... Ministry of Education and Research of Romania, Grant CNCSIS 187 8 Fixed Point Theory and Applications References [1] R P Agarwal, J Dshalalow, and D O’Regan, Fixed point and homotopy results ... operators (see [9, 15]) and they generalize some fixed point and strict fixed point principles for multivalued operators given in [3–5, 7, 8, 10–13] C Chifu and G Petrusel ¸ Fixed points Let (X,d) ... Frigon and Granas [6] See also Agarwal et al [1] and Chis and Precup [2] for some similar results or possi¸ bilities for extension Another fixed point result is the following C Chifu and G Petrusel...

Ngày tải lên: 22/06/2014, 22:20

... holds: (i) M is closed, cl(T(M)) is compact and I is continuous, (ii) M is bounded and complete, T is hemicompact and I is continuous, (iii) M is bounded and complete, T is condensing and I is continuous, ... (N) and if I is affine, then I satisfies the condition (C) and Tn (M) ⊂ I(M) provided T(M) ⊂ I(M) and q ∈ F(I) Corollary 2.3 Let M be a closed q-starshaped subset of a p-normed space X, and T and ... I and T be selfmaps of a Banach space X with u ∈ F(I) ∩ F(T), M ⊂ X with T(∂M ∩ M) ⊂ M Suppose that D is closed and q-starshaped with q ∈ F(I), I(D) = D, I is linear and continuous on D If I and...

Ngày tải lên: 22/06/2014, 22:20

... has been used in a variety of areas in differential equations and control theory (see Burton [2], Burton and Zhang [3], Balachandran and Sakthivel [1]) Theorem 2.1 (Schaefer) Let V be a normed ... φ(0), we obtain y (b) = γ, and so (1.1) is controllable on the interval J with u ∈ U This completes the proof 6 Fixed points and controllability in delay systems Examples and remarks In this section, ... + an Cn j , (3.17) Fixed points and controllability in delay systems |α| where Ci j is the cofactor of wi ,w j in the matrix ( wi ,w j )n×n , and for some positive constants and , we have n j...

Ngày tải lên: 22/06/2014, 22:20

... Fx ⊆ TX and Gx ⊆ SX for all x in X, and that 232 Fixed points and coincidence points for x, y in X, inequalities (3.4) and (3.5) are true Then {Sx : x ∈ X and Sx ∈ Fx} and {Tx : x ∈ X and Tx ∈ ... }, and inequality (3.9) is true for all x, y in X Then {Sx : x ∈ X and Sx ∈ Fx} and {Tx : x ∈ X and Tx ∈ Gx} are nonempty, closed sets and are equal Proof Let A = {Sx : x ∈ X and Sx ∈ Fx} and ... ϕ(0) = and A is a nonempty subset of X such that Fx ⊆ TA and Gx ⊆ SA for all x in A, and for x, y in A, inequalities (3.4) and (3.5) are true Then {Sx : x ∈ A and Sx ∈ Fx} = {T y : y ∈ A and T...

Ngày tải lên: 23/06/2014, 00:20

... Lip(L) = L , and so α(L) ≤ L and β(L) ≤ L A detailed account of the theory and applications of measures of noncompactness may be found in the monographs [1, 2] In view of conditions (a) and (b) of ... C[0,1] and L1 [0,1] (and all spaces into which they embed) not possess an unconditional basis The following proposition relates spaces with unconditional bases and spaces with monotone norm and ... Benavides, and G Lopez Acedo, Measures of Noncomı pactness in Metric Fixed Point Theory, Operator Theory: Advances and Applications, vol 99, Birkh¨ user Verlag, Basel, 1997 a Y Benyamini and Y Sternfeld,...

Ngày tải lên: 23/06/2014, 00:20

... that W is m -closed if W = W Each algebra is certainly 1 -closed and it is m -closed for all m iff it is Schurian Thus ∞ Wm = W∞ , Wm ⊃ Wm+1 m=1 where Wm (resp W∞ ) is the class of all m -closed (resp ... that (h1 )U = hU (h2 )U where h1 and h2 are the bijections associated with U1 and U2 , U = U1 ∩ U2 and hU , (h1 )U and (h2 )U are the bijections obtained from h, h1 and h2 by restriction to U Proof ... isomorphism In Sections and we prove Theorems 1.1 and 1.3, and Theorem 1.4 respectively Appendix contains the explicit description of the extended algebras of the direct sum and the wreath product...

Ngày tải lên: 07/08/2014, 06:20