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1
Content available Asymmetry in real functions theory
Jędrzejewski J. M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2018
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Vol. 23
11--24
EN
Since the beginning of the XX century many authors considered characterizations of local properties for real functions of a real variable which have been defined as global properties. We present a short survey of local properties of the well known global ones and consider of how small/big the set of asymmetrical behaviour of a function must be.
2
Content available On monotonicity of real functions
Jędrzejewski J. M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2017
|
Vol. 22
49--60
EN
Monotonicity of functions were of great interest of many mathematicians. Starting from the well known theorem of monotonicity of a differentiable function one can get quite sophisticated results. We give a survey of results when thesis of them is continuous and monotone function. Someone can ask why it should be continuous. Even a differentiable functions but not at the only point of its domain with positive derivative need not be non-decreasing. That is why we want to look for theorems for continuous functions.
3
Content available Profesor Tadeusz Świątkowski : dobry duch Politechniki Łódzkiej
Jóźwik I., Terepeta M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
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Vol. 19
277--286
PL
Profesor Tadeusz Świątkowski był wieloletnim pracownikiem i dyrektorem Instytutu Matematyki Politechniki Łódzkiej. Prezentujemy jego sylwetkę jako wielkiego matematyka i wspaniałego nauczyciela oraz jego wkład w rozwój teorii funkcji rzeczywistych.
4
Content available About differentiability and V BG * class
Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
245--249
EN
Let X be a finite dimensional real Banach space. We show that if the contingent of the curve Γ : (a, b) → X fulfils some conditions then each parametrization of that curve is V BG * . Stanisław Saks proved that each V BG * function is differentiable at a set of full Lebesgue measure. The result of this paper is a partial converse of that theorem.
5
Content available A note on weakly ϱ-upper continuous functions
Nowakowska K., Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
195--206
EN
In the article we present definition and some properties of weakly ϱ-upper continuous functions. We find maximal additive and maximal multiplicative families for the class of weakly ϱ-upper continuous functions.
6
Content available A mistake in definition of a limit of a function and some consequences
Jędrzejewski J. M., Kostrzewski T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
|
Vol. 19
61--65
EN
Many times our students make some errors in definitions, especially when we must apply some quantifiers. The definition of a limit is one of the definition with many quantifiers, so one can observe many mistakes in it. We want to present one of possible mistakes and show how to improve the understanding of this difficult but one of most important notions.
7
Content available A note on SI-spaces and MI-spaces
Ponomarev S. P.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2010
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Vol. 15
99--107
EN
We show that if there exists a second κ-category (or κ-Baire) SI-space, then there exists a second κ-category (resp. κ-Baire) MI-space. Next we discuss some properties of real functions on such spaces.
8
Content available On preponderantly continuous functions
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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Vol. 14
75-86
EN
In the present paper, a few different notions of preponderant continuity of a real function are discussed. We study the relationship between them and give some properties of preponderant continuity.
9
Content available remote On some properties of connected functions
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2008
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Vol. 13
15-26
EN
We consider some properties of functions defined in a topological space X with values in another topological space Y. We shall consider some properties of functions defined in a topological space X with values in a topological space Y. Topological terminology is taken from the books General Topology by R. Engelking [1] and General Topolowy by J. L. Kelley [7].
10
Content available remote A note on the quasicontinuity
Grande Z.
Demonstratio Mathematica
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2006
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Vol. 39, nr 3
515-518
EN
Let (X,px) and (V, pv) be metric spaces. A function f: X - Y is said graph quasicontinuous if there is a quasicontinuous function g : X -> Y with the graph Gr(g) contained in the closure cl(Gr(f)) of Gr(f). If the space (V, pv) is compact and if there is a dense subset A C X such that the restricted function f/A is continuous then f is graph quasicontinuous. Moreover each locally bounded function f: R -> R is graph quasicontinuous.
11
Content available remote On the equation associated with bounded paraconcave entropies
Dudek Z.
Demonstratio Mathematica
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2005
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Vol. 38, nr 2
401--411
EN
A paraconcave entropy function [2] is represented by a pair of two real functions of a real variable satisfying certain natural conditions. The subject of this paper is the functional equation, L(sum j f(pj)) = sum j g(pj)i, that describes equivalence between two representations of a paraconcave entropy function with concave functions f and g satisfying the condition for a bounded entropy. With the use of E-transforms of the functions f and g we reduce the problem of solvability of the equation to the problem ofinjectivity of a certain nonlinear operator denned on the set of concave homeomorphisms of the interval [0,1] onto itself. Additionally, we prove some facts about concavity of the E-transform f.
12
Content available remote On the coefficients of a class of univalent functions
Şerb I.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
567--578
EN
We consider a class of univalent functions which verify a strong Milin type condition for logarithmic coefficients. This class contains all alfa-Koebe spirallike functions, all extremal points of the class of typically real functions, together with their rotations and multiplicative "compositions". We find some extremal functions of this class.
13
Content available remote On the limits of functions of two variables
Grande M.
Demonstratio Mathematica
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2004
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Vol. 37, nr 2
309--315
EN
We show some conditions concerning sections of real functions of two variables which imply the existence of the double limit of considered function. Moreover we observe that the set of points, where the real function has the finite limit is an Cg-set and that a function having finite limit except a countable set is continuous except a countable set.
14
Content available remote Klasa funkcji o ograniczonej drugiej wariacji
Kostrzewski T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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1999
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Vol. 7
37--49
PL
Symbolem BC[a, b] będziemy oznaczać rodzinę funkcji, które są. różnicami dwóch funkcji wypukłych oraz spełniają pewne warunki regularnościowe na końcach przedziału [a, b]. W pracy omówiono pewne własności klasy BC[a, b] oraz jej związki z innymi klasami funkcji takimi, jak BV[a, b], Lip[a, b], klasą funkcji o ograniczonym wygięciu.
EN
By BC[a, b] we denote the set of all real functions defined on an interval [a, b] which are differences of two convex functions having finite one - sided derivatives at the points a and b. In this paper we investigate some properties of the function class BC[a, b] and the relation between this class and the other function class such as BV[a, b], Lip[a, b], functions of bounded bend.
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