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1
Content available remote

Complementary Results to Heuvers’s Characterization of Logarithmic Functions

100%
Himmel M.
Annales Mathematicae Silesianae
|
2017
|
tom 31
|
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.
2
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Riemann problem on the double of a multiply connected circular region

100%
Mityushev V.
Annales Polonici Mathematici
|
1997
|
tom 67
|
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.
3
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On continuous solutions of a functional equation

80%
Dankiewicz K.
Annales Polonici Mathematici
|
1996-1997
|
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.
4
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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.
5
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On a problem of Matkowski

80%
Daróczy Z., Maksa G.
Colloquium Mathematicum
|
1999
|
tom 82
|
nr 1
117-123
EN
We solve Matkowski's problem for strictly comparable quasi-arithmetic means.
6
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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.
7
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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.
8
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Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc

80%
Mityushev V.
Annales Polonici Mathematici
|
1998
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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.
9
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On the uniqueness of continuous solutions of functional equations

80%
Gaweł B.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 3
231-239
EN
We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities (1)   ψ(f(x)) ≤ β(x,ψ(x)) and (2)   α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)), where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation (3)  φ(f(x)) = g(x,φ(x)), where Y denotes an arbitrary metric space.
10
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The Abel equation and total solvability of linear functional equations

80%
Belitskii G., Lyubich Y.
Studia Mathematica
|
1998
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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.
11
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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 55
|
nr 2
EN
The distributivity law for a fuzzy implication \(I\colon [0,1]^2 \to [0,1]\) with respect to a fuzzy disjunction \(S\colon [0,1]^2 \to [0,1]\) 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: \( h(\min(xg(y),1)) = \min(h(x)+ h(xy),1)\), \(x \in (0,1)\), \(y \in (0,1]\), and \( h(xg(y)) = h(x)+ h(xy)\), \(x,y \in (0, \infty)\), in the class of increasing bijections \(h\colon [0,1] \to [0,1]\) with an increasing function \(g\colon (0,1] \to [1, \infty)\) and in the class of monotonic bijections \(h\colon (0, \infty) \to (0, \infty)\) with a function \(g\colon (0, \infty) \to (0, \infty)\), respectively. A description of solutions in more general classes of functions (including nonmeasurable ones) is presented.
12
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The law of large numbers and a functional equation

71%
Sablik M.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 2
165-175
EN
We deal with the linear functional equation (E) $g(x) = ∑^r_{i=1} p_i g(c_i x)$, where g:(0,∞) → (0,∞) is unknown, $(p₁,...,p_r)$ is a probability distribution, and $c_i$'s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli's Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
13
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A Generalization of m-Convexity and a Sandwich Theorem

61%
Lara T., Matkowski J., Merentes N., Quintero R., Wróbel M.
Annales Mathematicae Silesianae
|
2017
|
tom 31
|
nr 1
107-126
EN
Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.
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