Issue 2, Volume 27, August 2002

2002 · Open access

1. BILINEAR PROGRAMMING APPROACH TO OPTIMIZATION OVER THE EFFICIENT SET OF A VECTOR AFFINE FRACTIONAL PROBLEM LE DUNG MUU, HOANG QUANG TUYEN PDF

   ▸ Abstract

   We formulate the problem of optimizing a linear function over the weakly efficient set of a multicriteria affine fractional program as a special bilinear problem. For solving the latter problem, we propose a decomposition branch-and-bound algorithm taking into account the affine fractionality of the criterion function. The bounding uses only linear subprograms, the branching takes place over a simplex in the criteria space.

   119-139
2. FIXED POINTS OF CONVEX-VALUED GENERALIZED UPPER HEMICONTINUOUS MAPS, REVISITED SEHIE PARK PDF

   ▸ Abstract

   We give new fixed point theorems for a generalized upper hemicontinuous multimap whose domain and range may have different topologies. These include known theorems which appeared in nearly 50 published works.

   141-150
3. STRASSEN’S LOCAL LAW FOR DIFFUSION PROCESSES UNDER STRONG TOPOLOGIES M’HAMED EDDAHBI, MODESTE N’ZI PDF

   ▸ Abstract

   Under the assumption of pathwise uniqueness, we prove Strassen type functional local law of the iterated logarithm for solutions of stochastic differential equations in modulus spaces defined in term of the Young function $M_2(x) = \mathrm{exp}(x^2) − 1$ and the modulus of continuity $\varphi_0(t) = (t \log(1/t))^{1/2}$.

   151-163
4. ARCWISE CONNECTEDNESS OF THE SOLUTION SETS OF A SEMISTRICTLY QUASICONCAVE VECTOR MAXIMIZATION PROBLEM NGUYEN QUANG HUY PDF

   ▸ Abstract

   This paper presents some new facts on arcwise connectedness and contractibility of the solution sets in semistrictly quasiconcave vector maximization problems, where at least one of the objective functions is strictly quasiconcave.

   165-174
5. SOME GEOMETRIC PROPERTIES OF SPECIAL DOMAINS IN A BANACH SPACE LE TAI THU PDF

   175-183
6. APPROXIMATE RECOVERY OF MULTIVARIATE PERIODIC FUNCTIONS USING WAVELET DECOMPOSITIONS DINH DUNG, MAI XUAN THAO PDF

   ▸ Abstract

   We study the optimal recovery of multivariate periodic functions of the Besov class of common smoothness $SB^{\omega}_{p,\theta}$ from their values at $n$ points in terms of the quantity $R_n(SB^{\omega}_{p,\theta},L_q)$, which is a characterization of optimality of methods of recovery. The smoothness of $SB^{\omega}_{p,\theta}$ is defined via modulus of smoothness dominated by a function $\omega$ of modulus of smoothness type. With some restrictions on $\omega$ and $p, q$, we give the asymptotic order of this quantity when $n\to\infty$. An asymptotically optimal method of recovery is constructed by using the wavelet family formed from the integer translates of the dyadic scales of multivariate de la Vallée Poussin kernels.

   185-195
7. POLYNOMIAL MAPS OF THE COMPLEX PLANE WITH THE BRANCHED VALUE SETS ISOMORPHIC TO THE COMPLEX LINE NGUYEN VAN CHAU PDF

   ▸ Abstract

   We present a completed list of the polynomial dominating maps of $\mathbb C^2$ with the branched value curves isomorphic to the complex line $\mathbb C$, up to polynomial automorphisms.

   197-202
8. A REFINEMENT OF OSTROWSKI’S INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS S. S. DRAGOMIR PDF

   ▸ Abstract

   A refinement of the Ostrowski inequality obtained by Dragomir and Wang in [7] and applications for special means, quadrature formulae, cumulative distribution functions and Jeffreys divergence measure are given.

   203-217
9. EXTREME POINTS IN MUSIELAK-ORLICZ SEQUENCE SPACES S. SAEJUNG, S. DHOMPONGSA PDF

   ▸ Abstract

   This paper establishes some characterizations of extreme points and strongly extreme points of the closed unit ball in a Musielak-Orlicz sequence space equipped with the Luxemburg norm. As a consequence of these results, we obtain some geometric properties such as rotundity and strong rotundity in Nakano sequence spaces and Orlicz sequence spaces.

   219-229
10. ON A FIXED POINT THEOREM OF D. W. BOYD AND J. S. WONG MOHAMED AKKOUCHI PDF

    ▸ Abstract

    We present a generalization of a well-known fixed point theorem due to D. W. Boyd and J. S. Wong (see [3]). We also provide some improvements to this theorem.

    231-237
11. STRATIFICATION OF FAMILIES OF FUNCTIONS DEFINABLE IN O-MINIMAL STRUCTURES TA LÊ LOI PDF

    ▸ Abstract

    We prove the existence of Thom stratifications for families of functions definable in any o-minimal structure. The theory of o-minimal structures is a generalization of semi-algebraic and sub-analytic geometry. Our result implies Fukuda’s Theorem on the finiteness of topological types for polynomials on $\mathbb R^n$ with bounded degree.

    239-244