Showing papers in "Acta Mathematica Hungarica in 1975"
60 citations
TL;DR: In this paper, the convergence of R(f, x) holds for sufficiently large n's provided a.i.d., b.ii.d and b.iii.d.
Abstract: holds for sufficiently large n's provided a.=n -1/3, b.=n 2/3. Here co depends only on A and ~, and co2a (.) is the modulus of continuity o f f ( x ) on the interval [0, 2A]. As it was noted in [1], the convergence of R.(f , x) holds under the more general conditions a.=b./n~O, b . ~ o (rQ~oo) as well. The aim of the present paper is to improve the estimate (1) by an appropriate choice of a. and b. in the case when f (x ) satisfies some more restrictive conditions. Furthermore we shall show that these results can be applied to approximate certain improper integrals by quadrature sums of positive coefficients based on finite number of equidistant nodes. First we assume that f (x ) is uniformly continuous in [0, oo); then the modulus of continuity cos(. ) o f f ( x ) exists on the entire positive half-axis.
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TL;DR: In this article, the first class of Baire functions on the interval [0, 1] is defined and a set H c [ 0, 1] of points x 0, 1J is said to be an o~-zero set if there exists a function fEo ~ such that H = {x; f(x)=O}.
Abstract: 1.1. Let B 1 denote the first class of Baire on the interval [0, 1] and let ~ c B 1 be a class of Baire 1 functions containing the constants. A set H c [ 0 , 1] is said to be an o~-zero set if there exists a function fEo ~ such that H= {x; f(x)=O}. For eve ryXc [0, 1] let T~(X) denote the intersection of all ~--zero sets containing X. It is easy to see that if ~ forms a group with respect to the addition (i.e. f , gE~ implies f g E ~ ) then Ts~(X) coincides with the set of points x0E[0, 1J possessing the following property: if f , g E ~ and f(x)=g(x) holds for every xEX then f(xo) =g(x0).
TL;DR: In this article, a necessary and sufficient condition for the hereditariness and cohereditariness of a so-called C-class and D-class, respectively, was established.
Abstract: Dedicated to my teacher, Professor L Rddei on his 75 th birthday In this note we establish a necessary and sufficient condition for the hereditariness and cohereditariness of a so-called C-class and D-class, respectively In the ring theory a C-class and a D-class corresponds to a tad/ca1 class and a semisimple class, respectively As far as hereditary radicals are very common, homomorphically closed semisimple classes are very rare This fact shows that one of the conditions is a much stronger requirement than the other, ttiough they are categorically dual Investigating homomorphically closed semisimple classes we shall get a condition involving that a class of rings contains almost all simple rings (Corollary 1) For topological spaces and graphs C-classes and D-classes yield connectednesses and disconnectednesses, respectively It will turn out that hereditariness (cohereditariness) is almost incompatible with connectedness (disconnectedness) These considerations yield characterizations of the class of all T0-spaces (Corol~ary 6) and of the class of all graphs having at most one loop but with other edges (Corollary 8)
TL;DR: In this article, TURAN, SURANYI and BALAZS proved the following facts: if n = 2s then for any set of prescribed values e~,,, and fit, there is a uniquely determined polynomial.
Abstract: In [1]--[3] P. TURAN, J. SURANYI and J. BALAZS proved the following facts. Let us choose as fundamental points xg-=xk0 n of the (0, 2)-interpolation the zeros x,, ~ of the polynomials (t.3) Ii,,(x) = ( 1 xZ)P,;_~(x) where P, (x) stands for the n th Legendre polynomial with the normalization P , (1 )= 1. If n = 2s then for any set of prescribed values e~,,, and fit,, there is a uniquely determined polynomial
TL;DR: In this article, the error bounds for ZlAMAJ~mal's method were obtained without these assumptions. But these bounds are only satisfied if the boundary of R is sufficiently smooth (see [8] and [9]).
Abstract: Finite element methods using elements with curved sides are frequently applied to obtain approximate solutions of elliptic boundary value problems in a bounded open plane region R (see, for example, [1]--[7]). The finite element method suggested by ZLAMAJ~ (see [7]) has the iml?otant advantage that it gives directly the first partial derivatives of the solution of the boundary value problem. In Zl~imal's paper there are given error bounds for this method. In deriving the error bounds, however, it is assumed that the solution of the boundary value problem has square integrable third or fourth partial derivatives in R. These assumptions are satisfied, in general, only if the boundary of R is sufficiently smooth (see [8]--[9]). In the present paper we shall obtain error bounds for Zl~mal's method without these assumptions.