Showing papers in "Bulletin of The Korean Mathematical Society in 1999"

Condensing mappings and applications to existence theorems for common solution of differential equations

Abstract: In this paper some common fixed point theorems for pairs of condensing mappings in a Banach space are proved and applications are given to a pair of nonlinear first order ordinary differential equations in Banach spaces for proving the existence of common solution under suitable conditions.

Approximation in lipschitz algebras of infinitely differentiable functions

Abstract: We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

Controllability of second order semilinear volterra integrodifferential systems in banach spaces

Abstract: Sufficient conditions for controllability of semilinear second order Volterra integrodifferential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

Remarks on weak hypermodules

Abstract: -rings first were introduced by Vougiouklis in 1990 Then Darafsheh and the present author defined the -ring of fractions of a commutative hyperring The largest class of multivalued systems satisfying the module-like axioms is the Hv-module In this paper we define -module of fractions of a hypermodule Some interesting results concerning this -module is proved

Meromor0phic univalent harmonic functions with negative coefficients

Abstract: The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $z$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

On a functional equation associated with stochastic distance measures

Abstract: The general solution of the functional equation f1(pr, qs) + f2(ps, qr) = g(p,q) + h(r,s) for p, q, r, s ] 0, 1[will be investigated without any regularity assumptions on the unknown functions f1, f2, g, h:]0.1[->R.

FUZZY ${\gamma}$-PREOPEN SETS AND FUZZY ${\gamma}$-PRECONTINUOUS MAPS

Abstract: In this paper, we introduce the notions of fuzzy -peropen (-perclosed) sets and fuzzy -percontinuous (-peropen, -perclosed) maps, and investigate some of their properties.

Hardy-littlewood maximal functions in orlicz spaces

Abstract: Let Mf(x) be the Hardy-Littlewood maximal function on . Let and be functions satisfying (t) = a(s)ds and = b(s)ds, where a(s) and b(s) are positive continuous such that = and b(s) is quasi-increasing. We show that if there exists a constant so that for all , then there exists a constant such that(0.1) for all . Conversely, if there exists a constant satisfying the condition (0.1), then there exists a constant so that for all > 0 and .

On poly-eulerian numbers

Abstract: In this paper we difine poly-Euler numbers which generalize ordinary Euler numbers. We construct a p-adic poly-Euler measure by the poly-Euler polynomials and derive an integral formula.

A study on quasi-duo rings

Abstract: In this paper we study the connections between right quasi-duo rings and 2-primal rings, including several counterexamples for answers to some questions that occur naturally in the process. Actually we concern following three questions and modified ones: (1) Are right quasi-duo rings 2-primal, (2) Are formal power series rings over weakly right duo rings also weakly right duo\ulcorner and (3) Are 2-primal rings right quasi-duo\ulcorner Moreover we consider some conditions under which the answers of them may be affirmative, obtaining several results which are related to the questions.

Fibrewise infinite symmetric products and m-category

Abstract: Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration . The construction works for any commutative ring R with unit and is denoted by . For any pointed space B let be the i-th Ganea fibration. Defining admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then -cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.

Linear operators that preserve boolean ranks

Abstract: We consider the Boolean linear operators that preserve Boolean rank and obtain some characterizations of the linear operators which extend the results in [1].

Controllability of integrodifferential equations in banach spaces

Abstract: In this paper, we will study controllability of some case s an initial condition included in some approximated phase space. To this prove we used to the Schauder fixed point theorem.

Local derivations of the polynomial ring over a field

Abstract: In this article, we give an example of local derivation, that is not derivation, on the algebra F(x1,…, xn) of rational functions in x1, …, xn over an infinite field F, and show that if X is a set of symbols and {x1,…, xn} is a finite subset of X, n1, then each local derivation of F[x1,…, xn] into F[X] is a F-derivation and each local derivation of F[X] into itself is also a F-derivation.

A new characterization of ruled real hypersurfaces in complex space forms

Abstract: The purpose of this paper is to give another new characterization of ruled real hypersurfaces in a complex space form (c), c0 in terms of the covariant derivative of its Weingarten map in the direction of the structure vector .

Imbeddings of manifolds defined on an 0-minimal structure on (r,+,.,<)

Abstract: Let M be an 0-minimal structure on the standard structure :=( , +, ,rw) which are generalizations of Nash manifolds and Nash G manifolds. We prove that if M is polynomially bounded, then every Cr -G (0r) manifold is Cr -G imbeddable into some n, and that if M is exponential and G is a compact affine Cw -G group, then each compact -G imbeddable into some representation of G.

Large sieve for generalized trigonometric polynomials

Abstract: Generalized nonnegative trigonometric polynomials are defined as the products of nonnegative trigonometric polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We improve and extend the large sieve involving pth powers of trigonometric polynomials so that it holds for generalized trigonometric polynomials.

Average distances and octahedral norms

Abstract: In [6], Godefroy defined octahedral norms to give an isomorphic characterization of spaces containing . Here we will show that such norms can be defined by using "average distances" as introduced in[1]. Also, we indicate some other properties of average distances : in particular, we give some estimates for their values in the product of two spaces, furnished with the max or the sum norm.

Mixed volumes of a convex body and its polar dual

Abstract: In this paper, we obtain some geometric inequalities for mixed volumes of a convex body and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual.

Gottlieb groups on lens spaces

Abstract: In this paper we compute Gottlieb groups for generalized lens spaces. Then we apply this result to compute Gottlieb groups for total spaces of a principal torus bundle over a lens space.

Markov-bernstein type inequalitiies for polynomials

Abstract: Let (x) be an increasing function on the real line with finite moments of all oeders. We show that for any linear operator T on the space of polynomials and any interger n 0, there is a constant , independent of p(x), such that , for any polynomial p(x) of degree n, where We find a formular for the best possible value and estimations for . We also give several illustrating examples when T is a differentiation or a difference operator and (x) is an orthogonalizing measure for classical or discrete orthogonal polynomials.

THE VOLTERRA-STIELTJES INTEGRAL EQUATION AND THE OPERATOR-VALUED FUNCTION SPACE INTERGAL AS AN L(L_{p,}L_{p'}) THEORY

Abstract: In this note, we will prove that the operator-valued function space integral as an operator from (1

Real version of paley-wiener-schwartz theorem for ultradistributions with ultradifferentiable singular support

Abstract: We extend the Paley-Wiener-Schwartz theorem to the space of ultradistributions with respect to ultradifferentiable singular support and obtain its real version. That is, we obtain the growth condition in some tubular neighborhood of n of the Fourier transform of ultradistributions of Roumieu (or Beurling) type with ultradifferentiable singular support contained in a ball centered at the origin, and its real version.

v-PATHS OF ARCS IN REGULAR MULTIPARTITE TOURNAMENTS

Abstract: A v-path of an arc xy in a multipartite tournament T is an oriented oath in T-y which starts at x such that y does not dominate and end vertex of the path. We show that if T is a regular n-partite (n7) tournament, then every arc of T has a v-path of length m for all m satisfying 2mn-2. Our result extends the corresponding result for regular tournaments, due to Alspach, Reid and Roselle [2] in 1974, to regular multipartite tournaments.

Another characterization of round spheres

Abstract: A characterization of geodesic spheres in the simply connected space forms in terms of the ratio of the Gauss-Kronecker curvature and the (usual) mean curvature is given: An immersion of n dimensional compact oriented manifold without boundary into the n + 1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilicimmersion if the mean curvature does not vanish and the ratio / of the Gauss-Kronecker curvature and is constant.

ON THE DUALITY OF THE SPACE X AND THE ALGEBRA $C_p$(X)

Abstract: The set of continuous maps of a space X to real usual space R equipped with the toplogy of pointwise convergence will be denoted by (X). In this paper, we prove that; (X) is hereditarily separable and hereditary Lindelof if and only if is hereditarily separable and hereditary Lindelof.

On the countable compacta and expansive homeomorphisms

Abstract: In this paper we introduce the notions of expansive homeomorphism and its properties, and study the relation between countable compacta and ordinal numbers. Our results extend and improve those of T.Kimura and others.

Constructions for the sparsest orthogonal matrices

Abstract: In [1], it was shown that for the least number of nonzero entries in an orthogonal matrix is not direct summable is 4n-4, and zero patterns of the orthogonal matrices with exactly 4n-4 nonzero entries were determined. In this paper, we construct orthogonal matrices with exactly 4n-r nonzero entries. furthermore, we determine mn sparse row-orthogonal matrices.

Compatible pairs of orthogonal polynomials

Abstract: We find necessary and sufficient conditions for an or­ thogonal polynomial system to be compatible with another orthog­ onal polynomial system. As applications, we find new characteriza­ tions of semi-classical and classical orthogonal polynomials

Estimating convergence factors of Schwarz algorithms for orthogonal spline collocation method

Abstract: A new and simple estimate using a convex function for convergence factors of Schwarz algorithms orthogonal spline collocation method is presented. The estimated convergence factors in this context depend only on a way to split a given domain.