Issue 1, Volume 24, April 1999

1999 · Open access

1. ON A FIXED POINT THEOREM FOR NONEXPANSIVE NONLINEAR OPERATOR TRAN QUOC BINH, NGUYEN MINH CHUONG PDF

   ▸ Abstract

   A new generalized fixed point Edelstein's theorem and some results generalizing the ones of W. V. Petryshyn and T. E. Williamson
   [10] for nonexpansive and condensing mapping are proved.

   1-8
2. SUR LA COMPACITE DES SHIFTS A POIDS OPERATEURS MALIKA ABOUFATIMA, MOHAMED HOUIMDI PDF

   ▸ Abstract

   Soient $H$ un espace de Hilbert séparable complexe de di-mension infinie et $(e_n)_{n\geq 0}$ une base orthonormale de $H$. Soit $A$ le shift à poids défini par: $Ae_n=\alpha_ne_{n+1}$ où $(\alpha_n)_{n\geq 0}$ est une suite bornée de nombres complexes. Alors d'après [1] $A$ est compact si et seulement si $\lim_{n\to \infty}=0$. De plus, $A\in \mathcal C_p$ si et seulement si $\sum_{n\geq 0}|\alpha_n|^p < \infty$. Dans cet article on considère l'opérateur $A$ défini sur $H^{(\infty)}$ par: $A.(x_0,x_1,x_2,\dots)=(0,A_0x_0,A_1x_1,\dots)$ où $H^{(\infty)}$ est la somme directe hilbertienne d'une infinité dénombrable de copies de $H$ et où $(A_n)_{n\geq 0}$ est une suite d'opérateurs linéaires bornés sur $H$. On va montrer d'une part que $A$ compact si et seulement si pour tout $n,A_n$ est compact et $\lim_{n\to\infty} \| A_n\|=0$. D'autre part, $A\in \mathcal C_p$ si et seulement si pour tout $n\geq 0$ $A_n\in\mathcal C_p$ et $\sum_{n\geq 0} \| A_n \|_p^p < \infty$, où $\| .\|_p$ est la $\mathcal C_p$ norme.

   9-14
3. ON THE REGULARITY OF RANDOM MAPPINGS DANG HUNG THANG PDF

   ▸ Abstract

   In this paper, some regular properties of random mappings such as the stochastical continuity, the sample continuity and the measurability are investigated. The relation between the regularity and the problem of substituting the argument of a random mapping by a random variable is discussed.

   15-25
4. COMPLETENESS OF A COLLECTION GENERATED BY TRANSLATING A SET OF FUNCTIONS NGUYEN QUANG DIEU PDF

   ▸ Abstract

   Some sufficient conditions for completeness of a collections generated from translates and dilates of a single function in the functional spaces $L_p(\mathbb R^n)$, $C(\mathbb R^n)$, $C_0(\mathbb R^n)$ and in the subspace of all entire functions $C^{\infty}(\mathbb R^n)$ are given.

   27-38
5. AN AFFINE ALGEBRAIC TYPE OF THE PLÜCKER-MILNOR FORMULA ON $\mathbf{C}^2$ LE VAN THANH PDF

   ▸ Abstract

   The classical Plücker formulas are the relations between the order, class and genus of a given smooth projective algebraic plane curve which were first established by J. Plücker (1834) and later generalized by M. Noether (1875) for projective algebraic plane curves which may have ordinary singularities. A century later, these relations have been extended to the general case of projective algebraic curves by M. Rosenlicht (1952) and to the local case of analytical curves by Milnor (1968). In this note we shall establish such a relation for the affine case of algebraic plane curves.

   39-46
6. ON CONTINUITY PROPERTIES OF THE SOLUTION MAP IN QUADRATIC PROGRAMMING NGUYEN NANG TAM PDF

   ▸ Abstract

   We study in detail the lower semicontinuity and the upper semicontinuity properties of the set-valued map $(D,A,c,b)\to \mathrm{sol}(D,A,c,b),$ where $\mathrm{sol}(D,A,c,b)$ denotes the solution set of the quadratic programming problem
   $$\text{Minimize } f(x):=c^Tx+\dfrac 12 x^TDx \text{ subject to }Ax\geq b,\ x\geq 0.$$
   In particular, a complete characterization for the lower semicontinuity of the map $\mathrm{sol}(\cdot)$ is obtained.

   47-61
7. ON $(k + 1)$-DIMENSIONAL SPACE-LIKE RULED SURFACE IN THE MINKOWSKI SPACE MURAT TOSUN, ISMAIL AYDEMIR, NURI KURUO\v{G}LU PDF

   ▸ Abstract

   In this paper, we introduce the $(k+1)$-dimensional space-like ruled surfaces in Minkowski space $R^n_1$ and obtain interesting results related to asymptotic and tangential bundle of these spaces. Further, we give derivatives equations of these space-like ruled surfaces.

   63-74
8. ON SEGRE BOUND FOR THE REGULARITY INDEX OF FAT POINTS IN $\mathbf{P}^2$ PHAN VAN THIEN PDF

   ▸ Abstract

   In this paper we reprove Segre bound for the regularity index of fat points in $\mathbf{P}^2$ by a simple and natural method which may be used to study fat points in $\mathbf{P}^n$, $n\geq 3$.

   75-81
9. ON THE CONVERGENCE OF SOLUTIONS OF A SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS IN BANACH SPACES PHAM NGOC BOI PDF

   ▸ Abstract

   The main result of this paper shows the asymptotic behaviour of solutions to perturbed linear differential equations in Banach spaces.

   83-94
10. A UNIQUE RANGE SET OF P-ADIC MEROMORPHIC FUNCTIONS WITH 10 ELEMENTS PEI-CHU HU, CHUNG-CHUN YANG PDF

    ▸ Abstract

    In this paper, we will exhibit a unique range set for $p$-adic meromorphic functions with 10 elements.

    95-108
11. A REMARK ON VITUSHKIN'S COVERING NGUYEN VAN CHAU PDF

    ▸ Abstract

    It is shown that every polynomial map of the complex plane $\mathbb C^2$ with exceptional value set homeomorphic to the complex line $\mathbb C$ must have a singularity. This implies the nonexistence of Vitushkin's covering in the polynomial case.

    109-115