PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 30

Liczba wyników na stronie
first rewind previous Strona / 2 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  functional equation
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 2 next fast forward last
1
Content available Means in money exchange operations
Bojarski Jacek, Matkowski Janusz
Journal of Applied Mathematics and Computational Mechanics
|
2023
|
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.
2
On a solution to a functional equation
Patkowski Alexander E.
Journal of Applied Analysis
|
2022
|
Vol. 28, nr 1
91--93
EN
We offer a solution to a functional equation using properties of the Mellin transform. A new criteria for the Riemann Hypothesis is offered as an application of our main result, through a functional relationship with the Riemann xi function.
3
Content available Local stationary heat fields in fibrous composites
Baran Wojciech, Kurnik Krystian, Nawalaniec Wojciech, Shareif Albashir
Silesian Journal of Pure and Applied Mathematics
|
2019
|
vol. 9, iss. 1
1--8
EN
Consider a multiply connected domain D bounded by nonoverlapping circles. Introduce the complex potential u(z) = Re ϕ(z) in D where the function ϕ(z) is analytic in D except at infinity where ϕ(z) ∼ z. The function u(z) models the distribution of temperature in the domain D. The unknown function ϕ(z) is continuously differentiable in the closures of the considered domain. We solve approximately the modified Schwarz problem when u(z) = Re ϕ(z) is equal to an undetermined constant on every boundary component of D by a method of functional equations.
4
Content available remote On two functional equations connected with distributivity of fuzzy implications
Ger R., Kuczma M. E., Niemyska W.
Commentationes Mathematicae
|
2015
|
Vol 55, No. 2
163--169
EN
The distributivity law for a fuzzy implication I:[0,1]2→[0,1] with respect to a fuzzy disjunction S:[0,1]2→[0,1] states that the functional equation I(x,S(y,z))=S(I(x,y),I(x,z)) is satisfied for all pairs (x,y) from the unit square. To compare some results obtained while solving this equation in various classes of fuzzy implications, Wanda Niemyska has reduced the problem to the study of the following two functional equations: h(min(xg(y),1))=min(h(x)+h(xy),1), x∈(0,1), y∈(0,1], and h(xg(y))=h(x)+h(xy), x,y∈(0,∞), in the class of increasing bijections h:[0,1]→[0,1] with an increasing function g:(0,1]→[1,∞) and in the class of monotonic bijections h:(0,∞)→(0,∞) with a function g:(0,∞)→(0,∞), respectively. A description of solutions in more general classes of functions (including nonmeasurable ones) is presented.
5
Content available On some characterization of an inverse proportionality type function
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
175--178
EN
We deal with a functional equation of the form ƒ(x + y) = F(ƒ(x), ƒ(y)) (so called addition formula) assuming that the given binary operation F is associative but its domain is not connected. The aim of the present paper is to discuss solutions of the equation [formula]. It turns out that this functional equation characterized an inverse proportionality type function, but if the domain of the unknown function has no neutral element. In this paper we admit fairly general structure in the domain of the unknown function.
6
Content available Conjugate functions, lp-norm like functionals, the generalized Hölder inequality, Minkowski inequality and subhomogeneity
Matkowski J.
Opuscula Mathematica
|
2014
|
Vol. 34, no. 3
523-560
EN
For h : (0,∞) → R, the function h* (t) := th( 1/t ) is called (*)-conjugate to h. This conjugacy is related to the Hölder and Minkowski inequalities. Several properties of (*)-conjugacy are proved. If φ and φ* are bijections of (0,∞) then [formula]. Under some natural rate of growth conditions at 0 and ∞, if φ is increasing, convex, geometrically convex, then [formula] has the same properties. We show that the Young conjugate functions do not have this property. For a measure space (Ω,Σ,μ) denote by S = (Ω,Σ,μ) the space of all μ-integrable simple functions x : Ω → R, Given a bijection φ : (0,∞) → (0,∞) define [formula] by [formula] where Ω(x) is the support of x. Applying some properties of the (*) operation, we prove that if ƒ xy ≤ Pφ(x)Pψ (y) where [formula] and [formula] are conjugate, then φ and ψ are conjugate power functions. The existence of nonpower bijections φ and ψ with conjugate inverse functions [formula] such that Pφ and Pψ are subadditive and subhomogeneous is considered.
7
Content available remote A counterpart of the Taylor theorem and means
Matkowski J.
Fasciculi Mathematici
|
2014
|
Nr 53
85--93
EN
For an n-times differentiable real function ƒ defined in an a real interval I, some properties of the Taylor remainder means Tn[ƒ] are considered. It is proved that Tn[ƒ] is symmetric iff n – 1, and a conjecture concerning the equality Tn[g]- Tn[ƒ] is formulated. The main result says that if ƒ (n) is one-to-one, there exists a unique mean Mn[ƒ] : ƒ(n) (I) x ƒ(n) (I) → ƒ(n) (I) such that, for all x, y ϵ I, …[wzór]. The connection between Tnƒ ana Mnƒ is given. A functional equation related to M2 ƒ is derived and an open problem is posed.
8
Content available remote Single-valley-extended continuous solutions for the Feigenbaum's functional equation f (φ(x)) = φ2(f(x))
Zhang M.
Demonstratio Mathematica
|
2014
|
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.
9
Content available Utility functions invariant with respect to some classes of transformations
Chudziak J.
Control and Cybernetics
|
2013
|
Vol. 42, no. 2
347--363
EN
Inspired by some relevant recent results of A. E. Abbas we determine utility functions invariant with respect to some classes of transformations.
10
Content available The stability of the Dhombres-type trigonometric functional equation
Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
Vol. 17
87-96
EN
In the present paper we deal with the Dhombres-type trigonometric difference f(x + y 2 )2 – f(x − y 2)2 + f(x + y) + f(x − y) − f(x) [f(y) + g(y)], assuming that its absolute value is majorized by some constant. Our aim is to find functions and which satisfy the Dhombres-type trigonometric functional equation and for which the differences f - f and g - g are uniformly bounded.
11
Content available On some addition formulas for homographic type functions
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
Vol. 17
17-24
EN
We deal with the functional equation (so called addition formula) of the form f(x + y) = F(f(x),f(y)), where F is an associative rational function. The class of associative rational functions was described by A. Chéritat [1] and his work was followed by a paper of the author. For function F defined by F(x,y) = ϕ−1(ϕ(x) + ϕ(y)), where ϕ is a homographic function, the addition formula is fulfilled by homographic type functions. We consider the class of the associative rational functions defined by formula F(u,v) =uv αuv + u + v, where α is a fixed real numer.
12
Content available Solutions of the dhombres-type trigonometric functional equation
Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
Vol. 16
87--94
EN
Let (G, +) be a uniquely 2-divisible Abelian group. In the present paper we will consider the solutions of functional equation [f(x + y)]2 - [f(x - y)]2 + f(2x + 2y) + f(2x - 2y) = f(2x)[f(2y) + 2g(2y)], x,y ϵ G, where f and g are complex-valued functions defined on G.
13
Content available A characterization of a homographic type function II
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
Vol. 16
15--18
EN
This article is a continuation of the investigations contained in the previous paper [2]. We deal with the following conditional functional equation: [wzór] implies [wzór] with λ ≠ 0.
14
Content available On some generalizations of Gołąb-Schinzel functional equation
Matkowski J., Okrzesik J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2010
|
Vol. 15
81--90
EN
Composite functional equations in several variables generalizing the Gołąb-Schinzel equation are considerd and some simple methods allowing us to determine their one-to-one solutions, bijective solutions or the solutions having exactly one zero are presented. For an arbitrarily fixed real p, the functional equation Φ([pφ(y) + (1−p)]x +[(1−p)φ(x)+p]y) = φ(x)φ(y), x,y ∈ R, being a special generalization of the Gołąb-Schinzel equation, is considered.
15
Content available A characterization of a homographic type function
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2010
|
Vol. 15
25--30
EN
We deal with a functional equation of the form f(x + y) = F(f(x),f(y)) (the so called addition formula) assuming that the given binary operation F is associative but its domain of definition is not necessarily connected. In the present paper we shall restrict our consideration to the case when [formula]. These considerations may be viewed as counter parts of Losonczi's [7] and Domańska's [3] results on local solutions of the functional equation f(F(x, y)) = f(x) + f(y) with the same behaviour of the given associative operation F. In this paper we admit fairly general structure in the domain of the unknown function.
16
A composite functional equation and invariant curves
Matkowski J., Okrzesik J.
Journal of Applied Analysis
|
2010
|
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.
17
Content available On extension of solutions of a simultaneous system of iterative functional equations
Matkowski J.
Opuscula Mathematica
|
2009
|
Vol. 29, no. 4
415-421
EN
Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form φ(x)=h(x, φ[ƒ1(x)],…, φ[ƒm(x)]) φ(x)=H(x,φ[F1(x),…, [Fn(x)]) to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [1-3]).
18
Content available Extensions of solutions of a functional equation in two variables
Matkowski J.
Opuscula Mathematica
|
2009
|
Vol. 29, no. 4
423-425
EN
An extension theorem for the functional equation of several variables ƒ (M(x,y))=N(ƒ(x), ƒ (y)), where the given functions M and N are left-side autodistributive, is presented.
19
Content available remote Remarks on: "Oscillation criteria for second-order functional difference equation with neutral terms" [Demonstratio Math. 41 (2008)]
Karpuz B.
Demonstratio Mathematica
|
2009
|
Vol. 42, nr 3
549-551
EN
In this paper, we show that the paper mentioned in the title includes some wrong results. We also provide a counter example.
20
Content available remote On a sum form functional equation related to entropies and some moments of a discrete random variable
Nath P., Singh D.
Demonstratio Mathematica
|
2009
|
Vol. 42, nr 1
83-96
EN
The general solutions of a sum form functional equation have been obtained. The importance of its solutions in relation to the entropies and some moments of a discrete random variable has been discussed.
first rewind previous Strona / 2 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.