The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
In this paper we point out that in spite of the possibility of defining weak curves “filling” the closed unit ball $$B_{X}$$ of any normed space $$X$$ is optimum, the existence of a continuous linear functional which does not attain its sup on the closed unit ball of a non-reflexive Banach space (James’s theorem) allows us to find weak neighborhoods producing an anomalous behavior of the...
In this article, we expose some results related with Nikodym’s boundedness theorem. In particular, it is shown that, if Ω is a compact k-dimensional interval in the euclidean space $${\mathbb{R}^k}$$ , $${\mathcal{A}}$$ is the algebra of the subsets of Ω which are Jordan measurable and $${(\mathcal{A}_n)}$$ is an increasing sequence of subsets of $${\mathcal{A}}$$ , whose union is...
As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces (a’la Grothen-dieck) in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there is the class of Banach spaces including certain function spaces and sequence spaces which are distinguished by a poor geometrical structure...
Let A, B be nonempty subsets of a metric space (X, d) and T : A → 2B be a multivalued non-self-mapping. The purpose of this paper is to establish some theorems on the existence of a point $${x^*\in A}$$ , called best proximity point, which satisfies $${{\rm inf}\{d(x^*,y):y\in Tx^*\}=dist(A,B).}$$ This will be done for contraction multivalued non-self-mappings in metric spaces, as well...
Some new fixed point and common fixed point results for mappings in partial metric spaces are obtained. Various conditions such as Hardy–Rogers-type, quasicontraction type and weak contractive type conditions are used. Moreover, properties (P) and (Q) are investigated. Examples are presented to show how these results can be used.
Let {Xi, i ≥ 1} be a strictly stationary and positively associated sequence and let $${S_n = \sum_{i=1}^{n}X_i}$$ , $${M_n = \max_{1\leq j \leq n}|S_j|, |k_n| \leq C/ \log n}$$ for some C > 0 and $${\sigma^{2}:= EX_{1}^{2}+2 \sum_{i=2}^{\infty}EX_{1}X_{i}}$$ . By a maximal probability inequality established in this paper, the precise rate of a kind of weighted infinite series of...
Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise negatively orthant dependent random variables. Some sufficient conditions for strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables are presented without the assumption of identical distribution. Our results not only generalize the result of Sung (On the strong convergence for weighted sums of...
In a recent article, Yu and Clarke (J Stat Plan Inf 141:611–623, 2011) proposed to replace the expectation of the loss in statistical decision theory with the median of the loss. In particular, they proposed and investigated three possible criteria based on the median. In this article, the Bayes $${\varepsilon}$$ -quantloss criterion (a related but different criterion) is introduced and analyzed,...
The controlled branching process (CBP) is a generalization of the classical Bienaymé–Galton–Watson branching process, and, in the terminology of population dynamics, is used to describe the evolution of populations in which a control of the population size at each generation is needed. In this work, we deal with the problem of estimating the offspring distribution and its main parameters for a CBP...
Bayes spaces are vector spaces of sigma-additive positive measures. Proportional measures are considered equivalent and can be represented by densities with respect to a fixed dominating measure. The addition in these spaces is perturbation. It corresponds to Bayes theorem, which appears as a linear operation. Bayes spaces, with continuous dominating measures, contain finite and infinite measures...
In this paper, we introduce a new hybrid iterative process for finding a common element of the set of common fixed points of a finite family of nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove strong convergence of the proposed iterative process. The results we obtain extend and improve some recent known results.
We unify and extend several results on the dynamic behaviour of composition operators on the space of holomorphic functions on a simply connected plane domain and endowed with the compact open topology. In particular, we show that a composition operator is weakly supercyclic if and only if the algebra it generates consists entirely, except for the null one, of operators that are topologically mixing,...
We study the one parameter family of genus 2 Riemann surfaces defined by the orbit of the L-shaped translation surface tiled by three squares under the Teichmüller geodesic flow. These surfaces are real algebraic curves with three real components. We are interested in describing these surfaces by their period matrices. We show that the only Riemann surface in that family admitting a non-hyperelliptic...
In this paper, we establish tripled coincidence and common tripled fixed point theorems of Boyd–Wong and Matkowski type contractions. The presented theorems generalize and extend several well known comparable results in the literature, in particular the results of Samet and Vetro (for tripled case) [Ann Funct Anal 1(2):46–56, 2010]. We illustrate our obtained results by some examples.
In June 2010, we have the honor of seeing Prof Hironaka at Kyoto. He conjectures that the number $$d_2$$ is bounded under permissible blow-ups (see below). The next step is certainly to show that the number $$d_2$$ will drop under permissible blow-ups. Implicitly, the further conjectures about $$d_3,d_4,\ldots $$ will clarify the types of singularities under permissible blow-ups and...
In this paper, two sufficient conditions are provided for given two $$\mathcal K $$ -equivalent map-germs to be bi-Lipschitz $$\mathcal A $$ -equivalent. These are Lipschitz analogues of the known results on $$C^r$$ $$\mathcal A $$ -equivalence $$(0\le r\le \infty )$$ for given two $$\mathcal K $$ -equivalent map-germs. As a corollary of one of our results, a Lipschitz version...
We consider the affine real variety $$V=F^{-1}(0)$$ in $$\mathbf{R}^n$$ where $$F$$ is given by two quadratic forms. We announce several recent results, obtained in collaboration with various coauthors, about the topology of the generic $$V$$ and of its deformations $$V_t=F^{-1}(t)$$ , especially those that are smooth. This work started many years ago [16] with the case where...
A solution $$y(x)$$ of an Abel differential equation $$(1) \ y^{\prime }=p(x)y^2 + q(x) y^3$$ is called “closed” on $$[a,b]$$ if $$y(a)=y(b)$$ . The equation $$(1)$$ is said to have a center on $$[a,b]$$ if all its solutions (with the initial value $$y(a)$$ small enough) are closed. The problems of counting closed solutions (Smale–Pugh problem) is strongly related...
We associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on classical (compactly supported) homology with $$\mathbb Z _2$$ coefficients an analog of the weight filtration for complex algebraic varieties. This complements our previous definition of the weight filtration of Borel–Moore homology.
It has been recently shown that the iteration of Nash modification on not necessarily normal toric varieties corresponds to a purely combinatorial algorithm on the generators of the semigroup associated to the toric variety. We will show that for toric surfaces this algorithm stops for certain choices of affine charts of the Nash modification. In addition, we give a bound on the number of steps required...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.