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  1. 10 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
  2. 6 Annales Polonici Mathematici
  3. 6 Demonstratio Mathematica
  4. 4 Opuscula Mathematica
  5. 3 Journal of Applied Analysis
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  1. 1 2023
  2. 1 2022
  3. 2 2019
  4. 2 2017
  5. 1 2016
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  1. 8 Matkowski J.
  2. 5 Domańska K.
  3. 3 Mityushev V.
  4. 2 Ger R.
  5. 2 Kuczma M. E.
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1
Content available remote Riemann problem on the double of a multiply connected circular region
100%
Mityushev V.
Annales Polonici Mathematici
|
1997
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tom 67
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nr 1
1-14
EN
The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.
2
Content available remote Complementary Results to Heuvers’s Characterization of Logarithmic Functions
100%
Himmel M.
Annales Mathematicae Silesianae
|
2017
|
tom 31
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nr 1
99-106
EN
Based on a characterization of logarithmic functions due to Heuvers we develop analogous results for multiplicative, exponential and additive functions, respectively.
3
Content available remote Remarks on: "Oscillation criteria for second-order functional difference equation with neutral terms" [Demonstratio Math. 41 (2008)]
100%
Karpuz B.
Demonstratio Mathematica
|
2009
|
tom 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.
4
Content available Stability of the equation of homomorphism and completeness of the underlying space
80%
Moszner Z.
Opuscula Mathematica
|
2008
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tom Vol. 28, no. 1
83-92
EN
We prove that all assumptions of a Theorem of Forti and Schwaiger (cf. [4]) on the coherence of stability of the equation of homomorphism with the completeness of the space of values of all these homomorphisms, are essential. We give some generalizations of this theorem and certain examples of applications.
5
Extension theorem for a functional equation
80%
Burai P.
Journal of Applied Analysis
|
2006
|
tom Vol. 12, nr 2
293-299
EN
We are doing to prove an extension theorem on a functional equation for special means studied by Domsta and Matkowski
6
Content available remote On two functional equations connected with distributivity of fuzzy implications
80%
Ger R. , Kuczma M. E. , Niemyska W.
Commentationes Mathematicae
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2015
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tom 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.
7
Content available On extension of solutions of a simultaneous system of iterative functional equations
80%
Matkowski J.
Opuscula Mathematica
|
2009
|
tom 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]).
8
Content available Extensions of solutions of a functional equation in two variables
80%
Matkowski J.
Opuscula Mathematica
|
2009
|
tom 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.
9
Content available remote The Abel equation and total solvability of linear functional equations
80%
Belitskii G. , Lyubich Y.
Studia Mathematica
|
1998
|
tom 127
|
nr 1
81-97
EN
We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx) - φ(x) = γ(x). The smooth situation can also be considered in this way.
10
Content available remote On an extension of min-semistable distributions
80%
Ben Alaya M. , Huillet T. , Porzio A.
Probability and Mathematical Statistics
|
2007
|
tom Vol. 27, Fasc. 2
303--323
EN
This work focuses on a functional equation which extends the notion of min-semistable distributions. Our main results are an existence theorem and a characterization theorem for its solutions. The first establishes the existence of a class of solutions of this equation under a condition on the first zero on the positive axis of the associated structure function. The second shows that solutions belonging to a subclass of complementary distribution functions can be identified by their behavior at the origin. Our constructed solutions are in this subclass. The uniqueness question is also discussed.
11
Content available On some generalizations of Gołąb-Schinzel functional equation
80%
Matkowski J. , Okrzesik J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2010
|
tom 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.
12
Content available remote On a problem of Matkowski
80%
Daróczy Z. , Maksa G.
Colloquium Mathematicum
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1999
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tom 82
|
nr 1
117-123
EN
We solve Matkowski's problem for strictly comparable quasi-arithmetic means.
13
Content available remote Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc
80%
Mityushev V.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 3
227-236
EN
The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
14
Content available remote A counterpart of the Taylor theorem and means
80%
Matkowski J.
Fasciculi Mathematici
|
2014
|
tom 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.
15
Content available remote Continuous solutions of a polynomial-like iterative equation with variable coefficients
80%
Zhang W. , Baker J. A.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 1
29-36
EN
Using the fixed point theorems of Banach and Schauder we discuss the existence, uniqueness and stability of continuous solutions of a polynomial-like iterative equation with variable coefficients.
16
Content available A characterization of a homographic type function
80%
Domańska K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2010
|
tom 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.
17
On a solution to a functional equation
80%
Patkowski A. E.
Journal of Applied Analysis
|
2022
|
tom 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.
18
Content available On the superstability of the cosine and sine type functional equations
80%
Lehlou F. , Moussa M. , Roukbi A. , Kabbaj S.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
tom 15
EN
In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(x\sigma (y)a) + f(xya) = 2f(x)f(y)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f(x\sigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.
19
Content available remote On continuous solutions of a functional equation
80%
Dankiewicz K.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 2
151-156
EN
This paper discusses continuous solutions of the functional equation φ[f(x)] = g(x,φ(x)) in topological spaces.
20
Content available Cauchy type functional equations related to some associative rational functions
80%
Domańska K.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2019
|
tom 18
145-156
EN
L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.
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