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1
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On Baire measurable solutions of some functional equations

100%
Baron K.
Open Mathematics
|
2009
|
tom 7
|
nr 4
804-808
EN
We establish conditions under which Baire measurable solutions f of $$ \Gamma (x,y,|f(x) - f(y)|) = \Phi (x,y,f(x + \phi _1 (y)),...,f(x + \phi _N (y))) $$ defined on a metrizable topological group are continuous at zero.
2
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Marek Kuczma

100%
Baron K.
Banach Center Publications
|
2013
|
tom 99
|
nr 1
9-16
EN
The scientific output of Marek Kuczma consists of 179 papers published in the years 1958-1993 and three books still used and quoted. Professor Marek Kuczma created and developed the theory of iterative functional equations but his name is also connected to important results on functional equations in several variables, in particular on Cauchy's equation and Jensen's inequality. In fact Marek Kuczma has founded a mathematical school: he supervised 13 Ph.D. dissertations, 10 his students have already their habilitation and 6 of them became full professors. The paper provides more information about the great teacher and some results of the outstanding mathematician.
3
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On The Continuous Dependence Of Solutions To Orthogonal Additivity Problem On Given Functions

100%
Baron K.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
19-23
EN
We show that the solution to the orthogonal additivity problem in real inner product spaces depends continuously on the given function and provide an application of this fact.
4
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On orthogonally additive functions with orthogonally additive second iterate

100%
Baron K.
Commentationes Mathematicae
|
2013
|
tom 53
|
nr 2
EN
Let $\(E\) be a real inner product space of dimension at least 2. If \(f\) maps \(E\) onto \(E\) and both \(f\) and \(f \circ f \) are orthogonally additive, then \(f\) is additive.
5
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On Orthogonally Additive Functions With Big Graphs

100%
Baron K.
Annales Mathematicae Silesianae
|
2017
|
tom 31
|
nr 1
57-62
EN
Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.
6
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On orthogonally additive injections and surjections

100%
Baron K.
Commentationes Mathematicae
|
2015
|
tom 55
|
nr 2
EN
Let \(E\) be a real inner product space of dimension at least 2 and \(V\) a linear topological Hausdorff space. If \(\operatorname{card}E\leq \operatorname{card} V\), then the set of all orthogonally additive injections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology. If \(\operatorname{card}V\leq \operatorname{card}E\), then the set of all orthogonally additive surjections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology.
7
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Asymptotic properties of Markov operators defined by Volterra type integrals

64%
Baron K., Lasota A.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 2
161-175
EN
New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.
8
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Markov operators on the space of vector measures; coloured fractals

64%
Baron K., Lasota A.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 3
217-234
EN
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
9
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On the continuous solutions of a non-linear functional equation of the first order

50%
Baron K.
Annales Polonici Mathematici
|
1973
|
tom 28
|
nr 2
201-205
10
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Note on the existence of continuous solutions of a functional equation of n-th order

50%
Baron K.
Annales Polonici Mathematici
|
1974-1975
|
tom 30
|
nr 1
77-80
11
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On approximate solutions of a system of functional equations

44%
Baron K.
Annales Polonici Mathematici
|
1983
|
tom 43
|
nr 3
305-316
12
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Iteration of random-valued functions on the unit interval

38%
Baron K., Kuczma M.
Colloquium Mathematicum
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1977
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tom 37
|
nr 2
263-269
13
Content available remote

On the Cauchy equation modulo Z

38%
Baron K., Volkmann P.
Fundamenta Mathematicae
|
1988
|
tom 131
|
nr 2
143-148
14
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On Mikusiński-Pexider functional equation

32%
Baron K., Ger R.
Colloquium Mathematicum
|
1973
|
tom 28
|
nr 2
307-312
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