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1
Content available remote Solutions with big graph of the equation of invariant curves
100%
Bartłomiejczyk L.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2001
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tom Vol. 49, no 3
309-317
EN
We consider the functional equation of invariant curves [phi(f(x, phi(x))) = g(x, phi(x))] and we look for its solution which has a big graph. Such a graph is big from the point of view of topology and measure theory.
2
Content available remote Stability of n-dimensional additive functional equation in generalized 2-normed space
100%
Arunkumar M.
|
2016
|
tom Vol. 49, nr 3
319--330
EN
In this paper, the author established the general solution and generalized Ulam–Hyers–Rassias stability ofn-dimensional additive functional equation (…) in generalized 2-normed space.
3
Content available Propozycja wyzwalania twórczości matematycznej studentów przy pomocy pewnej nierówności funkcyjnej
100%
Fiduk E. , Siudut S.
|
2016
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tom 8
69-76
PL
T. Szostok and Sz. Wąsowicz in (Szostok, Wąsowicz, 2011) studied the following functional inequality: $\vert F\left( y \right)-F\left( x \right)-\left( y-x \right)f\left(\frac{x+y}{2} \right)\vert \le \varepsilon$ stemming from the Lagrange mean value theorem. They proved that the functon $f$ is affine, provided $f,F:\mathbb{R}\to \mathbb{R}$ satisfy the above inequality for all $x,y\in \mathbb{R}$. The aim of our paper is to extend the results of (Szostok, Wąsowicz, 2011) to more general situations (for example, we change $\mathbb{R}$ to $\mathbb{C}$ or $\mathbb{H})$.
4
Content available Propozycja wyzwalania twórczości matematycznej studentów przy pomocy pewnej nierówności funkcyjnej
100%
Fiduk E. , Siudut S.
|
2016
|
tom 8
69-76
PL
T. Szostok and Sz. Wąsowicz in (Szostok, Wąsowicz, 2011) studied the following functional inequality: $\vert F\left( y \right)-F\left( x \right)-\left( y-x \right)f\left(\frac{x+y}{2} \right)\vert \le \varepsilon$ stemming from the Lagrange mean value theorem. They proved that the functon $f$ is affine, provided $f,F:\mathbb{R}\to \mathbb{R}$ satisfy the above inequality for all $x,y\in \mathbb{R}$. The aim of our paper is to extend the results of (Szostok, Wąsowicz, 2011) to more general situations (for example, we change $\mathbb{R}$ to $\mathbb{C}$ or $\mathbb{H})$.
5
Content available remote Sur l'équation fonctionnelle f(x+y)=f(x)+f(y)
100%
Banach S.
Fundamenta Mathematicae
|
1920
|
tom 1
|
nr 1
123-124
FR
Le but de cette note est de démontrer que toute fonction mesurable f(x) satisfaisant à l'équation fonctionnelle f(x+y)=f(x)+f(y) est continue (donc, d'après Cauchy, de la forme Ax).
6
Content available remote Sur une propriété des fonctions de M. Hamel
88%
Sierpiński W.
Fundamenta Mathematicae
|
1924
|
tom 5
|
nr 1
334-336
FR
Le but de cette note est de démontrer le théorème suivant suggeré par Monsieur Nikodym: Théorème: Une fonction discontinue d'une variable réelle f(x) satisfaisant à l'équation fonctionnelle f(x+y) = f(x) + f(y), ne peut être majorée par aucune fonction mesurable.
7
Content available remote The stability of the second generalization of d'Alembert's functional equation
88%
Tyrała I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2008
|
tom Vol. 13
81-92
EN
In the present paper we study solutions of the second generalized d'Aleinbert's functional equation and its stability.
8
Content available remote Sur l'équation fonctionnelle f(x+y)=f(x)+f(y)
88%
Sierpiński W.
Fundamenta Mathematicae
|
1920
|
tom 1
|
nr 1
116-122
FR
Le but de cette note est de démontrer le théorème suivant: Toute fonction mesurable f(x) qui satisfait pour tous les nombres réels x et y à l'équation fonctionnelle f(x+y)=f(x)+f(y) est de la forme Ax où A est une constante.
9
Content available remote Homogeneous non-symmetric means of to variables
75%
Losonczi L.
|
2007
|
tom Vol. 40, nr 1
169-180
EN
Let f, g : I approaches R be given continuous functions on the interval I such that g is not equal to 0, and h := f/g is strictly monotonic (thus invertible) on I. Taking an increasing nonconstant functiong g ž on [0, 1].
10
Content available remote Positivity of Schilling functions
75%
Girgensohn R. , Morawiec J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2000
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tom Vol. 48, no 4
407-412
EN
We prove that every non-trivial [L^1]-solution of the Schilling problem is either positive or negative almost everywhere on its support.
11
Content available remote The stability of Fréchet’s equation
75%
Zdráhal T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1998
|
tom Vol. 4
16-21
EN
In this paper the Hyers - Ulam stability of Fréchet’s functional equation is dealt with. Our approach is motivated by results of L. Székelyhidi (see [2] and [3]) who pointed out that the classical Hyers's theorem on stability of this functional equation holds true (under an auxiliary hypothesis) for functions defined on amenable semigroups.
12
Content available remote On connections between oscillatory solutions of functional, difference and differential equations
75%
Nowakowska W. , Werbowski J.
Fasciculi Mathematici
|
2010
|
tom Nr 44
95-106
EN
The paper contains connections between oscillation of solutions of iterative functional equations, difference equations and differential equations with advanced or delayed arguments. New oscillatory criteria for these equations are given.
13
Content available remote Single-valley-extended continuous solutions for the Feigenbaum's functional equation f (φ(x)) = φ2(f(x))
75%
Zhang M.
Demonstratio Mathematica
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2014
|
tom Vol. 47, nr 3
615--626
EN
This work deals with the Feigenbaum's functional equation in the broad sense (…), where φ2 is the 2-fold iteration of φ, f(x) is a strictly increasing continuous function on [0, 1] and satisfies (...). Using constructive method, we discuss the existence of single-valley-extended continuous solutions of the above equation.
14
A composite functional equation and invariant curves
75%
Matkowski J. , Okrzesik J.
Journal of Applied Analysis
|
2010
|
tom Vol. 16, nr 1
121-133
EN
The continuous solutions of a composite functional equation are characterized. An applications to the problem of invariant curves is presented.
15
Content available Means in money exchange operations
63%
Bojarski J. , Matkowski J.
|
|
tom Vol. 22, nr 1
5--16
EN
It is observed that in some money exchange operations, every n-variable mean M applied by two market analysts who are acting in different countries should be self reciprocally conjugate. The main result says that the only homogeneous weighted quasi-arithmetic mean satisfying this condition is the weighted geometric mean. In the context of invariance of the geometric mean with respect to the arithmetic-harmonic mean-type mapping, the possibility of the occurring reciprocal-conjugacy in technical sciences is commented.
16
Content available remote On iterative roots of homeomorphisms of the circle
63%
Zdun M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2000
|
tom Vol. 48, no 2
203-213
EN
In this paper we deal with the problem of existence and uniqueness of continuous iterative roots of homeomorphisms of the circle. Let F : [S^1 --> S^1] be a homeomorphism without periodic points. If the limit set of the orbit [F^k(z), k belongs to Z] equals [S^1], then F has exactly n iterative roots of n-th order. Otherwise F either has no iterative roots of n-th order or F has infinitely many iterative roots depending on an arbitrary function. In this case we determined all iterative roots of n-th order of F.
17
Content available remote Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces
63%
EL-Fassi I. , Park C. , Kim G. H.
Demonstratio Mathematica
|
2018
|
tom Vol. 51, nr 1
295--303
EN
We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.
18
Content available remote Exponent in one of the variables
63%
Mityushev V.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom Vol. 12
77-79
EN
A periodicity functional equation of one complex variable which characterizes the exponential function is discussed. This functional equation can be generalized to equation for functions depending on two complex variables. It is conjectured that the second functional equation also characterizes the exponent. Applications to representations of complex continuous elementary functions are discussed.
19
Content available remote On new stability results for composite functional equations in quasi-β-normed spaces
63%
Thanyacharoen A. , Sintunavarat W.
|
|
tom Vol. 54, nr 1
68--84
EN
In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x) – f(y)) = f(x + y) + f(x – y) – f(x) – f(y), where f maps from a(β, p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s-functional inequality is discussed via our results.
20
Content available remote Stability of an additive-quadratic-quartic functional equation
63%
Kim G. H. , Lee Y.-H.
|
2020
|
tom Vol. 53, nr 1
1--7
EN
In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x-2y) - 2f(x+y) - 2f(-x-y) - 2f(x-y) - 2f(y-x)+4f(-x)+2f(x) - f(2y) - f(-2y)+4f(y)+4f(-y)=0 by the direct method in the sense of Găvruta.
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