Papers by Janusz Matkowski
Mathematica Slovaca, Jun 1, 2013
Assuming that the involved functions are three times differentiable, we determine all Bajraktarev... more Assuming that the involved functions are three times differentiable, we determine all Bajraktarević means which are invariant respect to the mean-type mapping of the Beckenbach-Gini mean type. Some applications in iteration theory and functional equation are presented.
Demonstratio Mathematica, 1995
Composition operator, representation formula of globally Lipschitzian operator, the Banach spaces... more Composition operator, representation formula of globally Lipschitzian operator, the Banach spaces, C n (/), polynomials of the degree at most n.
Journal of Mathematical Analysis and Applications, Dec 1, 2011
The problem of invariant curves for continuous mean-type mappings is considered. The obtained res... more The problem of invariant curves for continuous mean-type mappings is considered. The obtained results are applied in solving some functional equations.
Journal of Mathematical Analysis and Applications, Dec 1, 2008
Let (Ω, Σ, μ) a measure space such that 0 < μ(A) < 1 < μ(B) < ∞ for some A, B ∈ Σ. Under some nat... more Let (Ω, Σ, μ) a measure space such that 0 < μ(A) < 1 < μ(B) < ∞ for some A, B ∈ Σ. Under some natural conditions on the bijective functions ϕ, ϕ for all nonnegative μ-integrable simple functions x, y : Ω → R (where Ω(x) stands for the support of x, then there exists a real p 1 such that Some generalizations and relevant results for the reversed inequality are also presented.
Geometrically Convex Solutions of Certain Difference Equations and Generalized Bohr-Mollerup Type Theorems
Resultate der Mathematik, Nov 1, 1994
ABSTRACT
On a generalization of mulholland’s inequality
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, Dec 1, 1993
Let (f2, E, #) be a measure space such that #(A) = 0 or #(A) &amp;gt; 1 for every A c E. We p... more Let (f2, E, #) be a measure space such that #(A) = 0 or #(A) &amp;gt; 1 for every A c E. We prove among others that if q~ is a convex homeomorphism of (0, oo) such that the function log o~b o exp is convex in R then
Journal of Mathematical Analysis and Applications, Dec 1, 1997
Let , , ␥ ,  : 0, ϱ ª R, strictly monotonic and continuous functions, be the generators of the p... more Let , , ␥ ,  : 0, ϱ ª R, strictly monotonic and continuous functions, be the generators of the positively homogeneous quasi-arithmetic means M , M , M , ␥ and M . The main result gives full characterizations of the functions , , ␥ , and   such that M M x, y , M x, y sM x, y , x, y)0.
Journal of Mathematical Analysis and Applications, 2011
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library 137 (2012) MATHEMATICA BOHEMICA No. 4,[415][416][417][418][419][420][421][422][423]
Uniformly continuous superposition operators in the space of bounded variation functions
Mathematische Nachrichten, May 12, 2010
ABSTRACT
An invariance of the geometric mean with respect to Stolarsky mean-type mappings
Results in Mathematics, Feb 1, 2003
ABSTRACT
On a Characterization of Lipschitzian Operators of Substitution in the SpaceBV{a, b)
Mathematische Nachrichten, 1984
Invariant and complementary quasi-arithmetic means
Aequationes Mathematicae, Feb 1, 1999
Summary. Let $ I\subset {\Bbb R} $ be an interval. Under the assumptions that $ \phi, \psi, \gamm... more Summary. Let $ I\subset {\Bbb R} $ be an interval. Under the assumptions that $ \phi, \psi, \gamma :I \rightarrow {\Bbb R} $ are one-to-one, $ \gamma(I) $ is an interval, and at least one of the functions $ \phi \circ \gamma^{-1} $, $ \psi \circ \gamma ^{-1} $ is twice continuously differentiable on $ \gamma(I) $, we determine all
Sitzungsberichte und Anzeiger der mathematisch-naturwissenschaftlichen Klasse, 2005
In this note we introduce a one-parameter family of homogeneous means strictly related to ellipse... more In this note we introduce a one-parameter family of homogeneous means strictly related to ellipses. Each member of the family is a weighted power mean, and only one of them is both symmetric and quasi-arithmetic. Geometric interpretations are given, and higher-dimensional counterparts of these means are defined. Iterations of some mean-type mappings and some functional equations are considered.
Square iterative roots of generalized weighted quasi-arithmetic mean-type mappings
Acta Mathematica Hungarica, Feb 1, 2021
We determine all pairs $$(A_{f,g},A_{g,h})$$ ( A f , g , A g , h ) of generalized weighted quasi-... more We determine all pairs $$(A_{f,g},A_{g,h})$$ ( A f , g , A g , h ) of generalized weighted quasi-arithmetic means being square iterative roots of $$(A_{F,G},A_{G,H})$$ ( A F , G , A G , H ) , that is, the equation \begin{equation*} ( A_{f,g},A_{g,h}) \circ ( A_{f,g},A_{g,h}) =(A_{F,G},A_{G,H}), \end{equation*} is solved under three times differentiability of the functions $$f, g, h, F, G, H$$ f , g , h , F , G , H . As an application, some special cases are presented.
Commentationes Mathematicae, 2010
Assume that the generator of a Nemytskii composition operator is a function of three variables: t... more Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener ϕ-variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.
Journal of Inequalities in Pure & Applied Mathematics, 2007
It is shown that, under some algebraic conditions on fixed reals α1, α2, . . . , αn+1 and vectors... more It is shown that, under some algebraic conditions on fixed reals α1, α2, . . . , αn+1 and vectors a1, a 2 , . . . , a n+1 ∈ R n , every continuous at a point function f : R n → R satisfying the simultaneous system of inequalities has to be of the form f (x) = p • x + f (0), x ∈ R n , with uniquely determined p ∈ R n . For mappings with values in a Banach space which are weakly of a constant sign, a counterpart of this result is given.
On a characterization of $L^p$-norm
Annales Polonici Mathematici, 1989
Journal of Mathematical Analysis and Applications, Sep 1, 2005
We determine the class of all pairs of the Lagrangian means forming mean-type mappings which are ... more We determine the class of all pairs of the Lagrangian means forming mean-type mappings which are invariant with respect to the arithmetic mean.
ESAIM, Apr 1, 2012
Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, . . . , Mp : I p... more Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, . . . , Mp : I p → I the continuous means. We consider the problem of invariance of the graphs of functions ϕ : J p-1 → I with respect to the mean-type mapping M = (M1, . . . , Mp) . Applying a result on the existence and uniqueness of an M-invariant mean [7], we prove that if the graph of a continuous function ϕ : J p-1 → I is M-invariant, then ϕ satises a simple functional equation. As a conclusion we obtain a theorem which, in particular, allows to determine all the continuous and decreasing in each variable functions ϕ of the M-invariant graphs. This improves some recent results on invariant curves where the case p = 2 is considered.
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Papers by Janusz Matkowski