共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we first establish some existence theorems of systems of generalized vector equilibrium problems. From these
results, we obtain new variants of Ekeland’s variational principle in a Hausdorff t.v.s., a minimax theorem and minimization
theorems. Some applications to the existence theorem of systems of semi-infinite problem, a variant of flower petal theorem
and a generalization of Schauder’s fixed point theorem are also given. 相似文献
2.
Murat Limoncu 《Archiv der Mathematik》2010,95(2):191-199
By using two modified Ricci tensors, we prove some theorems which correspond to Myers’s diameter estimate theorem and Bochner’s
vanishing theorem. 相似文献
3.
In this paper, we consider a generalized system in real Banach spaces. Using Brouwer’s fixed-point theorem, we establish some
existence theorems for generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity for a bifunction and extend Minty’s lemma for a generalized system. Furthermore, using the Minty
lemma and KKM-Fan lemma, we establish an existence theorem for a generalized system with monotonicity in real reflexive Banach
spaces. 相似文献
4.
Deng Hua ZHANG Huai Xin CAO 《数学学报(英文版)》2007,23(2):321-326
We prove a generalization of Hyers' theorem on the stability of approximately additive mapping and a generalization of Badora's theorem on an approximate ring homomorphism. We also obtain a more general stability theorem, which gives the stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems given in this paper follow essentially the D. H. Hyers-Th. M. Rassias approach to the stability of functional equations connected with S. M. Ulam's problem. 相似文献
5.
Some theorems from inversive and Euclidean circle geometry are extended to all affine Cayley-Klein planes. In particular,
we obtain an analogue to the first step of Clifford’s chain of theorems, a statement related to Napoleon’s theorem, extensions
of Wood’s theorem on similar-perspective triangles and of the known fact that the three radical axes of three given circles
are parallel or have a point in common. For proving these statements, we use generalized complex numbers.
Supported by a grant D01-761/24.10.06 from the Ministry of Education and Sciences, and by a grant 108/2007 from Sofia University. 相似文献
6.
N. Amenta 《Discrete and Computational Geometry》1994,12(1):241-261
Recent combinatorial algorithms for linear programming can also be applied to certain nonlinear problems. We call these Generalized Linear-Programming, or GLP, problems. We connect this class to a collection of results from combinatorial geometry called Helly-type theorems. We show that there is a Helly-type theorem about the constraint set of every GLP problem. Given a familyH of sets with a Helly-type theorem, we give a paradigm for finding whether the intersection ofH is empty, by formulating the question as a GLP problem. This leads to many applications, including linear expected time algorithms for finding line transversals and mini-max hyperplane fitting. Our applications include GLP problems with the surprising property that the constraints are nonconvex or even disconnected. 相似文献
7.
Joel Spencer 《Combinatorica》1981,1(3):303-307
We compare extremal theorems such as Turán’s theorem with their corresponding partition theorems such as Ramsey’s theorem.
We derive a general inequality involving chromatic number and independence number of symmetric hypergraphs. We give applications
to Ramsey numbers and to van der Waerden numbers. 相似文献
8.
By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational
principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by
the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement
of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev
theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization
theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other. 相似文献
9.
Extreme properties of quermassintegrals of convex bodies 总被引:3,自引:0,他引:3
In this paper, we establish two theorems for the quermassintegrals of convex bodies, which are the generalizations of the
well-known Aleksandrov’ s projection theorem and Loomis-Whitney’ s inequality, respectively. Applying these two theorems,
we obtain a number of inequalities for the volumes of projections of convex bodies. Besides, we introduce the concept of the
perturbation element of a convex body, and prove an extreme property of it. 相似文献
10.
In this paper, we attempt to give a unified approach to the existing several versions of Ekeland’s variational principle.
In the framework of uniform spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type
of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance (particularly, a p-distance),
which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized
Takahashi’s nonconvex minimization theorem, a generalized Ekeland’s variational principle and a generalized Caristi’s fixed
point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland’s
variational principle, we deduce a number of particular versions of Ekeland’s principle, which include many known versions
of the principle and their improvements. 相似文献
11.
Daniel Dufresne Jose Garrido Manuel Morales 《Methodology and Computing in Applied Probability》2009,11(3):359-383
Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected
value of max (S – K, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In
this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship
with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical
examples are provided.
相似文献
12.
Veraverbeke’s (Stoch Proc Appl 5:27–37, 1977) theorem relates the tail of the distribution of the supremum of a random walk with negative drift to the tail of the distribution
of its increments, or equivalently, the probability that a centered random walk with heavy-tail increments hits a moving linear
boundary. We study similar problems for more general processes. In particular, we derive an analogue of Veraverbeke’s theorem
for fractional integrated ARMA models without prehistoric influence, when the innovations have regularly varying tails. Furthermore,
we prove some limit theorems for the trajectory of the process, conditionally on a large maximum. Those results are obtained
by using a general scheme of proof which we present in some detail and should be of value in other related problems. 相似文献
13.
The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular
function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions
and for M-convex/concave functions as generalizations of Frank’s discrete separation theorem for submodular/supermodular set
functions and Edmonds’ matroid intersection theorem. This paper shows the equivalence between Murota’s L-convex functions
and Favati and Tardella’s submodular integrally convex functions, and also gives alternative proofs of the separation theorems
that provide a geometric insight by relating them to the ordinary separation theorem in convex analysis.
Received: November 27, 1997 / Accepted: December 16, 1999?Published online May 12, 2000 相似文献
14.
We show that the ‘pseudoconcave holes’ of some naturally arising class of manifolds, called hyperconcave ends, can be filled
in, including the case of complex dimension two. As a consequence we obtain a stronger version of the compactification theorem
of Siu-Yau and extend Nadel’s theorems to dimension two.
Mathematics Subject Classification (1991) 32J05, 32C22, 53C55 相似文献
15.
The main purpose of this paper is to study spectral and B-Fredholm properties of a multiplierT acting on a semi-simple regular tauberian commutative Banach algebraA. We show thatT is a B-Fredholm operator if and only ifT is a semi B-Fredholm operator, and in this case we have the indexind(T)=0. Moreover we give some spectral properties for multipliers. Spectral mapping theorems for the Weyl’s and B-Weyl spectrum
of a multiplier are also considered. Furthermore we show that Weyl’s theorem and generalized Weyl’s theorem hold for a multiplierT. Finally we give sufficient conditions for a multiplier to be a product of an invertible and an idempotent operators. 相似文献
16.
M. Frigon 《Journal of Fixed Point Theory and Applications》2011,10(2):279-298
We give generalizations in complete gauge spaces of the following results: Bishop-Phelps’ theorem, Ekeland’s variational principle,
Caristi’s fixed point theorem, the drop theorem and the flower petal theorem. We show that our generalizations are equivalent.
We apply those results to obtain fixed point theorems for multivalued contractions defined on a closed subset of a complete
gauge space and satisfying a generalized inwardness condition. 相似文献
17.
S. Raghavan 《Proceedings Mathematical Sciences》1984,93(2-3):147-160
Recently, Bombieri and Vaaler obtained an interesting adelic formulation of the first and the second theorems of Minkowski
in the Geometry of Numbers and derived an effective formulation of the well-known “Siegel’s lemma” on the size of integral
solutions of linear equations. In a similar context involving linearinequalities, this paper is concerned with an analogue of a theorem of Khintchine on integral solutions for inequalities arising from
systems of linear forms and also with an analogue of a Kronecker-type theorem with regard to euclidean frames of integral
vectors. The proof of the former theorem invokes Bombieri-Vaaler’s adelic formulation of Minkowski’s theorem. 相似文献
18.
In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman’s theorem, Roth’s theorem and Petryshyn’s theorem are extended to condensing mappings satisfying the interior condition. 相似文献
19.
Memudu O. Olatinwo 《Central European Journal of Mathematics》2008,6(2):335-341
In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts
of an A—distance and an E—distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type.
Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of
Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].
相似文献
20.
Carathéodory’s, Helly’s and Radon’s theorems are three basic results in discrete geometry. Their max-plus or tropical analogues
have been proved by various authors. We show that more advanced results in discrete geometry also have max-plus analogues,
namely, the colorful Carathéodory theorem and the Tverberg theorem. A conjecture connected to the Tverberg theorem—Sierksma’s
conjecture—although still open for the usual convexity, is shown to be true in the max-plus setting. 相似文献