共查询到20条相似文献,搜索用时 484 毫秒
1.
In the present work we prove a coincidence point theorem in Menger spaces with a t-norm T which satisfies the condition sup{T(t,t):t<1}=1. As a corollary of our theorem we obtain some existing results in metric spaces and probabilistic metric spaces. Particularly our result implies a probabilistic generalization of Banach contraction mapping theorem. We also support our result by an example. 相似文献
2.
A characterization of n-dimensional spaces via continuous selections avoiding Z
n
-sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem, and to obtain a new alternative proof of the Hurewicz formula. It is also shown that our selection theorem yields an easy proof of a Michael's result. 相似文献
3.
A. Van Daele 《代数通讯》2013,41(6):2341-2386
A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups. 相似文献
4.
Alexej P. Pynko 《Archive for Mathematical Logic》2006,45(3):267-305
In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style
interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case,
a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation
theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without
equality from those with equality. From the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation
theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation
symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also
apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general
propositional logic. 相似文献
5.
In this paper we will obtain a Stone type theorem under the frame of Hilbert C*-module, such that the classical Stone theorem is our special case. Then we use it as a main tool to obtain a spectrum decomposition theorem of certain stationary quantum stochastic process. In the end, we will give it an interpretation in statistical mechanics of multi-linear response. 相似文献
6.
Xia Chen 《Journal of Theoretical Probability》1997,10(3):695-732
A theorem on the law of the iterated logarithm is established for m-dependent B-valued random variables. The conditions in our theorem match their independent analogues and appear as necessary or minimal for the results. According to an example given in the paper, the situation we face is much different from the finite dimensional case and therefore, so is the way we solve the problems. 相似文献
7.
As a consequence of our main result, a theorem of Schrijver and Seymour that determines the zero sum Ramsey numbers for the family of all r-hypertrees on m edges and a theorem of Bialostocki and Dierker that determines the zero sum Ramsey numbers for r-hypermatchings are combined into a single theorem. Another consequence is the determination of zero sum Ramsey numbers of multiple copies of some small graphs. 相似文献
8.
t -intersecting k-chains in posets using the kernel method. These results are common generalizations of the original EKR and HM theorems, and
our earlier results for intersecting k-chains in the Boolean algebra. For intersecting k-chains in the c-truncated Boolean algebra we also prove an exact EKR type theorem (for all n) using the shift method. An application of the general theorem gives a similar result for t-intersecting chains if n is large enough.
Received November 20, 1997 相似文献
9.
A sup-preserving map f between complete lattices L and M is regular if there exists a sup-preserving map g from M to L such that fgf=f. In the class of completely distributive lattices, this paper demonstrates a necessary and sufficient condition for f to be regular. When L=M is a power set, our theorem reduces to the well known Zareckiĭ’s theorem which characterizes regular elements in the semigroup
of all binary relations on a set. Another application of our result is a generalization of Zareckiĭ’s theorem for quantale-valued
relations. 相似文献
10.
K. Peter Cass 《Mathematische Nachrichten》1996,177(1):5-7
Our concern is to find a representation theorem for operators in B(c(X), c(Y)) where X and Y are Banach spaces with Y containing an isomorphic copy of c0. Cass and Gao [1] obtained a representation theorem that always applies if Y does not contain an isomorphic copy of c0. Maddox [3], Melvin - Melvin [4], and Robinson [5] consider operators in B(c(X), c(Y)) that are given by matrices. In this paper we show that Cass's and Gao's result in [1] can be extended, when Y contains an isomorphic copy of c0, to certain operators that we call represent able. In addition, we show that when Y contains an isomorphic copy of co there are always operators that fall outside the scope of our representation theorem. Light is also cast on a theorem given in Maddox [3, Theorem 4.2] and [5, Theorem IV]. 相似文献
11.
In this paper, we introduce an iterative sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim.
14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory
106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem. 相似文献
12.
Jari Taskinen 《Israel Journal of Mathematics》1995,92(1-3):207-219
We prove a universal mapping theorem for “integral” holomorphic mappings on the open unit ball ofC(K). In our theorem, the universal space isC(K), and the universal mapping is increasing in the positive cone ofC(K). 相似文献
13.
Sehie Park 《Journal of Applied Mathematics and Computing》2000,7(1):1-28
In the present paper, we introduce fundamental results in the KKM theory for G-convex spaces which are equivalent to the Brouwer theorem, the Sperner lemma, and the KKM theorem. Those results are all abstract versions of known corresponding ones for convex subsets of topological vector spaces. Some earlier applications of those results are indicated. Finally, we give a new proof of the Himmelberg fixed point theorem andG-convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory. 相似文献
14.
N. A. Watson 《Rendiconti del Circolo Matematico di Palermo》1988,37(1):150-160
We study the behaviour of certain hyperplane mean values of solutions of parabolic equations on an infinite strip, and use
our results to prove a representation theorem for solutions which satisfy a one-sidedL
p constraint. 相似文献
15.
Anton Freund 《PAMM》2016,16(1):903-904
A fundamental question in mathematical logic asks: What are the minimal assumptions and deduction principles required to prove a particular theorem? Now consider the special case of a theorem that can be established by checking a finite number of decidable cases — think of a single instance of the finite Ramsey theorem. In this particular situation the answer to our question is trivial: The theorem can be demonstrated by an explicit verification, thus without the use of any “strong” proof principles. This answer, however, is not very satisfying: An explicit verification may be unfeasible if there is an enormous number of cases to check. At the same time there might be a short and meaningful proof using stronger proof methods. Such a situation suggests a modified question: What are the minimal assumptions and deduction principles required for a reasonably short proof of the given theorem? Our contribution explores this question for instances of the Paris-Harrington principle. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
A. B. Levy 《Mathematical Programming》1996,74(3):333-350
We study implicit multifunctions (set-valued mappings) obtained from inclusions of the form 0∈M(p,x), whereM is a multifunction. Our basic implicit multifunction theorem provides an approximation for a generalized derivative of the
implicit multifunction in terms of the derivative of the multifunctionM. Our primary focus is on three special cases of inclusions 0∈M(p,x) which represent different kinds of generalized variational inequalities, called “variational conditions”. Appropriate versions
of our basic implicit multifunction theorem yield approximations for generalized derivatives of the solutions to each kind
of variational condition. We characterize a well-known generalized Lipschitz property in terms of generalized derivatives,
and use our implicit multifunction theorems to state sufficient conditions (and necessary in one case) for solutions of variational
conditions to possess this Lipschitz, property. We apply our results to a general parameterized nonlinear programming problem,
and derive a new second-order condition which guarantees that the stationary points associated with the Karush-Kuhn-Tucker
conditions exhibit generalized Lipschitz continuity with respect to the parameter. 相似文献
17.
Gabriel Acosta María G. Armentano Ricardo G. Durn Ariel L. Lombardi 《Journal of Mathematical Analysis and Applications》2005,310(2):397-411
In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1(Ω) using the Lax–Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1(Ω) does not apply, in fact the restriction of H1(Ω) functions is not necessarily in L2(∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2(Ω) and we obtain an a priori estimate for the second derivatives of the solution. 相似文献
18.
Xie Ping DING 《数学学报(英文版)》2006,22(5):1529-1538
A new class of locally finite continuous topological spaces (for short, locally FC-spaces) and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures. 相似文献
19.
Laura De Carli 《Israel Journal of Mathematics》2000,118(1):15-27
In this paper we prove a unique continuation theorem for elliptic operators of the formP(D)+V(x), whereP(D) has orderm≥2 and simple complex characteristics, andV(x)∈L
n/m
(R
n
). To prove our main theorem we use a restriction theorem for the Fourier transform to manifolds of codimension 2. 相似文献
20.
Daniel Dubischar 《Probability Theory and Related Fields》2002,123(4):601-605
Let {P
n
, n ?ℕ} be a sequence of Borel probability measures on a compact and connected metric space X. We show that in case the measures P
n
converge weakly to a fully supported limit measure P, there exist uniformly converging random variables X
n
, n ?ℕ with these given laws. Connectivity and compactness are necessary conditions for our theorem to hold. We also present a decent
generalization. We prove our theorem by means of a comparison of the Prokhorov and the so-called minimal L
∞
metric. Then we only need to use the Strassen-Dudley theorem and Kellerer's measure extension theorem for decomposable families.
Received: 2 November 2000 / Revised version: 5 January 2002/ Published online: 1 July 2002 相似文献