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.
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.
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.
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Przedstawiono nową metodę aproksymacji skończonego układu punktów płaszczyzny, zawierającego punkty "odstające" od układu. Dotychczas proponowane metody eliminowały te punkty, a pozostały układ aproksymowały prostą. W opisanej metodzie nie odrzuca się żadnego punktu. Jako krzywą aproksymującą przyjęto figurę będącą sumą punktu i prostej i wyznaczono jej parametry. Otrzymana w ten sposób prosta - nazwana odporną prostą regresji - jest uniezależniona od "odstających" punktów, które opisuje wyznaczony punkt. Metodę zilustrowano przykładami.
EN
Approximation of the plane point finite system is not only a theoretical problem. It exists also in engineering and economy. The points on the plane are the result of investigation and experience. So, it is highly probable to obtain results - point that are :not congruent" with the others. Sometimes it happens just accidentally, it may, however, be also the evidence of some anomalies. In this article, we consider a finite plane points the system dispersed along the straight line, including the points "not congruent" with the system. While seeking the regression curve describing a given plane point system, we often ask ourselves to that extent the curve course is influence by those "not congruent" points. The method proposed previously assumed that the curve course is not influenced by those substantially by those "not congruent" points and approximation the whole system by straight line or eliminated those points and the remaining system was approximated by the straight line. In the method described below no points is rejected. As an approximating curve there was assumed a figure being the sum of point and straight lines, and afterwards its parameter were determined. The straight line obtained in this way - called the resistant regression line - does not depend on the "not congruent" points described by the point determined. The method is illustrated by examples calculating each time - for comparison - the residstant regression straight line and regression straight line.
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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.
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