共查询到20条相似文献,搜索用时 15 毫秒
1.
Tomás Domínguez Benavides 《Journal of Mathematical Analysis and Applications》1985,105(1):176-186
Let X be a Banach space, C a bounded closed subset of X, A a convex closed subset of X, a complete metric space formed by all α-nonexpansive mappings fC → A and a complete metric space formed by α-nonexpansive differentiable mappings fC → X. The following assertions are proved in this paper: (1) Properness of I ? f is a generic property in (2)the subset of formed by all α-contractive mappings is of Baire first category in ; and (3) for every y?X, the functional equation x ? f(x) = y has generically a finite number of solutions for f in . Some applications to the fixed point theory and calculation of the topological degree are given. 相似文献
2.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1980,76(2):339-368
We show that, if (F →uX) is a linear system, a convex target set and a convex functional, then, under suitable assumptions, the computation of inf ) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of , or of the infima on F of Lagrangians, involving elements of . Also, we prove similar results for a convex system (F →uX) and the convex cone Ω of all non-positive elements in X. 相似文献
3.
Let G be a subset of a locally convex separated topological vector space E with int(G) ≠ Ø, cl(G) convex and quasi-complete. Let f: cl(G) → E be a continuous condensing multifunction with compact and convex values and with a bounded range. It is shown that for each w? int(G), there exists a u = u(w) ??(cl(G)) such that p(f(u) ? u) = inf{p(x ? y): x?f(u), y? cl(G)}, where p is the Minkowski's functional of the set (cl(G) ? w). Several fixed point results are obtained as a consequence of this result. 相似文献
4.
Zahava Shmuely 《Journal of Combinatorial Theory, Series A》1976,21(3):369-383
The (isotone) map f: X → X is an increasing (decreasing) operator on the poset X if f(x) ? f2(x) (f2(x) ? f(x), resp.) holds for each x ∈ X. Properties of increasing (decreasing) operators on complete lattices are studied and shown to extend and clarify those of closure (resp. anticlosure) operators. The notion of the decreasing closure, , (the increasing anticlosure, ,) of the map f: X → X is introduced extending that of the transitive closure, , of f. , and are all shown to have the same set of fixed points. Our results enable us to solve some problems raised by H. Crapo. In particular, the order structure of H(X), the set of retraction operators on X is analyzed. For X a complete lattice H(X) is shown to be a complete lattice in the pointwise partial order. We conclude by claiming that it is the increasing-decreasing character of the identity maps which yields the peculiar properties of Galois connections. This is done by defining a u-v connection between the posets X and Y, where u: X → X (v: Y → Y) is an increasing (resp. decreasing) operator to be a pair f, g of maps f; X → Y, g: Y → X such that gf ? u, fg ? v. It is shown that the whole theory of Galois connections can be carried over to u-v connections. 相似文献
5.
The following result, and a closely related one, is proved: If u:X → Y is an open, perfect surjection, with X metrizable and with dim X = 0 or dim Y = 0, then there exists a perfect surjection such that u ° h = πY (where S in the Cantor set and is the projection). If moreover, u-1(y) is homeomorphic to S for all y?Y, then h can be chosen to be a homeomorphism. 相似文献
6.
Douglas Hensley 《Journal of Number Theory》1985,21(3):286-298
The number defined by the title is denoted by Ψ(x, y). Let and let ?(u) be the function determined by ?(u) = 1, 0 ≤ u ≤ 1, u?′(u) = ? ?(u ? 1), u > 1. We prove the following:Theorem. For x sufficiently large and log y ≥ (log log x)2, Ψ(x,y) ? x?(u) while for 1 + log log x ≤ log y ≤ (log log x)2, and ε > 0, .The proof uses a weighted lower approximation to Ψ(x, y), a reinterpretation of this sum in probability terminology, and ultimately large-deviation methods plus the Berry-Esseen theorem. 相似文献
7.
Igor Kluvánek 《Journal of Functional Analysis》1976,21(3):316-329
For a set K in a locally convex topological vector space X there exists a set T, a σ-algebra of subsets of T and a σ-additive measure m: → X such that K is the closed convex hull of the range {m(E): E ∈ } of the measure m if and only if there exists a conical measure u on X so that K Ku,Ku, the set of resultants of all conical measures v on X such that v < u. 相似文献
8.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1981,81(2):437-452
We show that if F, X are two locally convex spaces and are two convex functionals satisfying h(y) = ?(y, x0) (y?F) for some x0?X, then, under suitable assumptions, the computation of inf h(F) can be reduced to the computation of inf ?(H) on certain hyperplanes H of F × X. We give some applications. 相似文献
9.
J Globevnik 《Journal of Functional Analysis》1976,22(1):32-38
Denote by Δ(resp. ) the open (resp. closed) unit disc in C. Let E be a closed subset of the unit circle T and let F be a relatively closed subset of T ? E of Lesbesgue measure zero. The following result is proved. Given a complex Banach space X and a bounded continuous function f:F → X, there exists an extension f? of f, bounded and continuous on , analytic on Δ and satisfying sup. This is applied to show that for any separable complex Banach space X there exists an analytic function from Δ to X whose range is contained and dense in the unit ball of X. 相似文献
10.
Claudio Morales 《Journal of Mathematical Analysis and Applications》1985,105(1):167-175
Let X be a Banach space with the dual space to be uniformly convex, let D ? X be open, and let be strongly accretive (i.e., for some k < 1: (λ ? k)∥ u ? v∥ ? ∥(λ ? 1)(u ? v)+ T(u) ? T(v)∥ for all and λ > k). Suppose T is demicontinuous and strongly accretive and suppose there exists z?D satisfying: T(x) t(x ? z) for all x??D and t < 0. Then it is shown that T has a unique zero in . This result is then applied to the study of existence of zeros of accretive mappings under apparently different types of boundary conditions on T. 相似文献
11.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
12.
Samuel M Rankin 《Journal of Mathematical Analysis and Applications》1982,88(2):531-542
Existence and asymptotic behavior of solutions are given for the equation u′(t) = ?A(t)u(t) + F(t,ut) (t ? 0) and u0 = ? ? C([?r,0]; X) C. The space X is a Banach space; the family of unbounded linear operators defined on D(A) ? X → X generates a linear evolution system and F: C → X is continuous with respect to a fractional power of A(t0) for some t0 ? [0, T]. 相似文献
13.
David M. Mason 《Stochastic Processes and their Applications》1983,15(1):99-109
Let Gn denote the empirical distribution based on n independent uniform (0, 1) random variables. The asymptotic distribution of the supremum of weighted discrepancies between Gn(u) and u of the forms 6wv(u)Dn(u)6 and 6wv(Gn(u))Dn(u)6, where Dn(u) = Gn(u)?u, wv(u) = (u(1?u))?1+v and 0 ? v < is obtained. Goodness-of-fit tests based on these statistics are shown to be asymptotically sensitive only in the extreme tails of a distribution, which is exactly where such statistics that use a weight function wv with ? v ? 1 are insensitive. For this reason weighted discrepancies which use the weight function wv with 0 ? v < are potentially applicable in the construction of confidence contours for the extreme tails of a distribution. 相似文献
14.
Ronald E Bruck 《Journal of Mathematical Analysis and Applications》1980,76(1):159-173
We show that if u is a bounded solution on + of u″(t) ?Au(t) + f(t), where A is a maximal monotone operator on a real Hilbert space H and f∈Lloc2(+;H) is periodic, then there exists a periodic solution ω of the differential equation such that u(t) ? ω(t) 0 and u′(t) ? ω′(t) → 0 as t → ∞. We also show that the two-point boundary value problem for this equation has a unique solution for boundary values in and that a smoothing effect takes place. 相似文献
15.
We characterize complete Hausdorff locally convex solid lattices (E,τ) satisfying the following property: for all operators such that 0?S?T and T precompact, the operator S2 is precompact. To cite this article: B. Aqzzouz, R. Nouira, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
16.
Richard Askey Deborah Tepper Haimo 《Journal of Mathematical Analysis and Applications》1977,59(1):119-129
We study degeneration for ? → + 0 of the two-point boundary value problems , and convergence of the operators T?+ and T?? on 2(?1, 1) connected with them, T?±u := τ?±u for all for all . Here ? is a small positive parameter, λ a complex “spectral” parameter; a, b and c are real ∞-functions, a(x) ? γ > 0 for all x? [?1, 1] and h is a sufficiently smooth complex function. We prove that the limits of the eigenvalues of T?+ and of T?? are the negative and nonpositive integers respectively by comparison of the general case to the special case in which a 1 and b c 0 and in which we can compute the limits exactly. We show that (T?+ ? λ)?1 converges for ? → +0 strongly to (T0+ ? λ)?1 if . In an analogous way, we define the operator T?+, n (n ? in the Sobolev space H0?n(? 1, 1) as a restriction of τ?+ and prove strong convergence of (T+?,n ? λ)?1 for ? → +0 in this space of distributions if . With aid of the maximum principle we infer from this that, if h?1, the solution of τ?+u ? λu = h, u(±1) = A ± B converges for ? → +0 uniformly on [?1, ? ?] ∪ [?, 1] to the solution of xu′ ? λu = h, u(±1) = A ± B for each p > 0 and for each λ ? if ? ?.Finally we prove by duality that the solution of τ??u ? λu = h converges to a definite solution of the reduced equation uniformly on each compact subset of (?1, 0) ∪ (0, 1) if h is sufficiently smooth and if 1 ? ?. 相似文献
17.
P.S Milojević 《Journal of Mathematical Analysis and Applications》1978,65(2):468-502
Let X and Y be real normed spaces with an admissible scheme Γ = {En, Vn; Fn, Wn} and T: X → 2YA-proper with respect to Γ such that dist(y, A(x)) < kc(∥ x ∥) for all y in T(x) with ∥ x ∥ ? R for some R > 0 and k > 0, where c: R+ → R+ is a given function and A: X → 2Y a suitable possibly not A-proper mapping. Under the assumption that either T or A is odd or that (u, Kx) ? 0 for all u in T(x) with , we obtain (in a constructive way) various generalizations of the first Fredholm theorem. The unique approximation-solvability results for the equation T(x) = f with T such that T(x) ? T(y) ?A(x ? y) for x, y in X or T is Fréchet differentiable are also established. The abstract results for A-proper mappings are then applied to the (constructive) solvability of some boundary value problems for quasilinear elliptic equations. Some of our results include the results of Lasota, Lasota-Opial, Hess, Ne?as, Petryshyn, and Babu?ka. 相似文献
18.
In this paper we study linear differential systems (1) matrix-valued function defined on the k-torus Tk and (θ, t) → θ + ωt is a given irrational twist flow on Tk. First, we show that if A ? CN(Tk), where N ? {0, 1, 2,…; ∞; ω}, then the spectral subbundles are of class CN on Tk. Next we assume that à is sufficiently smooth on Tk and ω satisfies a suitable “small divisors” inequality. We show that if (1) satisfies the “full spectrum” assumption, then there is a quasi-periodic linear change of variables x = P(t)y that transforms (1) to a constant coefficient system y′ =By. Finally, we study the case where the matrix in (1) is the Jacobian matrix of a nonlinear vector field evaluated along a quasi-periodic solution x = φ(t) of (2) . We give sufficient conditions in terms of smoothness and small divisors inequalities in order that there is a coordinate system (z, ?) defined in the vicinity of , the hull of φ, so that the linearized system (1) can be represented in the form z′ = Dz, ?′ = ω, where D is a constant matrix. Our results represent substantial improvements over known methods because we do not require that à be “close to” a constant coefficient system. 相似文献
19.
20.
Colin M. Ramsay 《Insurance: Mathematics and Economics》1984,3(2):139-143
Let {T1, Y1}∞i=1 be a sequence of positive independent random variables. Let, also, Z1 = βY′1 ? πTi, i = 1, 2, …, where Y′1 = Max(0, Yi ? w), w ? 0, and where β < 0 and π is such that E(Z1) < 0. We consider the random walk of partial sums Sn = ?ni=1Zi in the presence of an absorbing region (u, ∞), u ? 0, and S0 ≡ 0. Of interest is where S? = Sup(0, S1, S2, …, Sn, …). 相似文献