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K-continuity problem of K-superquadratic set-valued functions

Troczka-Pawelec K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

227--235

In this paper we study K-superquadratic set-valued functions.We will present here some connections between K-boundedness of K-superquadratic set-valued functions and K-semicontinuity of multifunctions of this kind.

K-continuity of K-subquadratic set-valued functions

Troczka-Pawelec K., Tyrala I.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2014

Vol. 19

237--244

Let X = (X, +) be an arbitrary topological group. A set-valued function F : X → n(Y) is called K-subquadratic if 2F(s) + 2F(t) ⊂ F(s + t) + F(s - t) + K, for all s, t ϵ X, where Y denotes a topological vector space and where K is a cone in this space. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to weakly K-boundedness. The case where Y = R N will be considered separately.

On approximation of subquadratic functions by quadratic functions

Troczka-Pawelec K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

79--86

In this paper we establish an approximation of subquadratic functions, which satisfy the condition ∃ ϵ > 0 ∀ x ϵ X |ϕ(2x) - 4ϕ(x)| ≤ 3ϵ, by quadratic functions.

Equations with Parameter Solved in Cabri Geometry

Rys P., Zdráhal T.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

187--190

In this contribution a method for graphical solving any quadratic equation as well as a method for graphing quadratic functions by means of the Cabri Geometry is shown. The goal is to provide high school 's students with the visual idea how parameter in both equations and functions is doing.

Asymptotic properties of the ANOVA test under general loss functions

Adamczyk Katarzyna

Matematyka Stosowana : matematyka dla społeczeństwa

1993

Nr 36

75--97

The author studies the classical analysis of variance problem under nonnormal distributions involving a location parameter (so that these distributions really do not involve an unknown variance). The quadratic function in the analysis of variance decomposition is replaced by a convex even function w, and the asymptotic distribution of the corresponding test statistic under the null hypothesis is found to be a chi-squared distribution. Several specific choices of w are considered in detail.