Janusz Matkowski
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View article: Restrictive Lipschitz continuity, basis property of a real sequence, and fixed-point principle in metrically convex spaces
Restrictive Lipschitz continuity, basis property of a real sequence, and fixed-point principle in metrically convex spaces Open
A mapping T of a metric space $$\left( X,d\right) $$ into a metric space $$ \left( Y,\rho \right) $$ is called restrictive Lipschitz if there exist: a positive decreasing to zero sequence $$\left( t_{n}:n\in \mathbb {N} \right) $…
View article: Explicit forms of invariant means: complementary results to Gauss $$\left( {\mathcal {A}},{\mathcal {G}}\right) $$-theorem and some applications
Explicit forms of invariant means: complementary results to Gauss $$\left( {\mathcal {A}},{\mathcal {G}}\right) $$-theorem and some applications Open
Explicit forms of invariant means for all mean-type mappings generated by the bivariable classical arithmetic, geometric and harmonic means (complementary to the Gauss $$\mathcal {AGM}$$ -theorem) are given. A generalization for higher d…
View article: A generalization of the Goebel–Kirk fixed point theorem for asymptotically nonexpansive mappings
A generalization of the Goebel–Kirk fixed point theorem for asymptotically nonexpansive mappings Open
Some results extending the Goebel–Kirk fixed point theorem for asymptotically nonexpansive mappings are presented.
View article: On Weak Generalized Stability of Random Variables via Functional Equations
On Weak Generalized Stability of Random Variables via Functional Equations Open
In this paper we characterize random variables which are stable but not strictly stable in the sense of generalized convolution. We generalize the results obtained in Jarczyk and Misiewicz (J Theoret Probab 22:482-505, 2009), Misiewicz and…
View article: Subcommutativity of integrals and quasi-arithmetic means
Subcommutativity of integrals and quasi-arithmetic means Open
Let $(X, \mathscr{L}, λ)$ and $(Y, \mathscr{M}, μ)$ be finite measure spaces for which there exist $A \in \mathscr{L}$ and $B \in \mathscr{M}$ with either $0 < λ(A) < 1 < λ(X)$ and $0 < μ(B) < μ(Y)$, or the other way around. In addition, l…
View article: Means in money exchange operations
Means in money exchange operations Open
Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of T…
View article: A refinement of the Browder–Göhde–Kirk fixed point theorem and some applications
A refinement of the Browder–Göhde–Kirk fixed point theorem and some applications Open
The following generalization of the Browder–Göhde–Kirk fixed point theorem is proved: if C is a nonempty bounded closed and convex subset of a uniformly convex normed space X and T is a self-mapping of C such that $$\left\| Tx-Ty\right\| \…
View article: Quasi-Cauchy quotients and means
Quasi-Cauchy quotients and means Open
Let $$I\subset {\mathbb {R}}$$ be an interval that is closed under addition, and $$ k\in {\mathbb {N}}$$ , $$k\ge 2\,$$ . For a function $$f:I\rightarrow \left( 0,\infty \right) $$ such that $$F\left( x\right) :=\f…
View article: Complementary means with respect to a nonsymmetric invariant mean
Complementary means with respect to a nonsymmetric invariant mean Open
It is known that if a bivariate mean K is symmetric, continuous and strictly increasing in each variable, then for every mean M there is a unique mean $$N\,$$ such that K is invariant with respect to the mean-type mapping $$\left( M,N\rig…
View article: Means in money exchange operations
Means in money exchange operations Open
It is observed that in some money exchange operations, the applied $n$ -variable mean $M$ should be self reciprocally-conjugate, i.e. it should satisfy the equality \[ M\left( x_{1},\ldots,x_{n}\right) M\left( \frac{1}{x_{1}},\ldots,\frac{…
View article: Mean-type mappings and invariance principle
Mean-type mappings and invariance principle Open
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an i…
View article: On the Beckenbach–Gini–Lehmer Means and Means Mappings
On the Beckenbach–Gini–Lehmer Means and Means Mappings Open
Beckenbacg–Gini–Lehmer type means and mean-type mappings generated by functions of several variables, for which the arithmetic mean is invariant, are introduced. Equality of means of that type, their homogeneity, and convergence of the ite…
View article: Remarks on submultiplicative functions
Remarks on submultiplicative functions Open
The real functions satisfying the inequality Ф (uv) ≤ KФ (u) Ф (v) for some positive K which occur among others in [5], [3], [4], and referred there as submultiplicative, are discussed. A simplifying remark that Ф satisfies this inequality…
View article: Generalization of the Harmonic Weighted Mean Via Pythagorean Invariance Identity and Application
Generalization of the Harmonic Weighted Mean Via Pythagorean Invariance Identity and Application Open
Under some simple conditions on the real functions f and g defined on an interval I ⊂ (0, ∞ ), the two-place functions A f ( x, y ) = f ( x ) + y − f ( y ) and G g ( x , y ) = g ( x ) g ( y ) y {G_g}\left({x,y} \right) …
View article: Sandwich results for periodicity and conjugacy
Sandwich results for periodicity and conjugacy Open
Let P be a nonconstant selfmap of a set $$\mathcal {M}$$ . A sandwich-type theorem for generalized sub- P -periodic functions defined on $$\mathcal {M}$$ with values in a reflexive Banach space is proved. In particular, given functions $…
View article: The logarithmic Cauchy quotient mean
The logarithmic Cauchy quotient mean Open
Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.
View article: The logarithmic Cauchy quotient mean
The logarithmic Cauchy quotient mean Open
Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.
View article: Invariant means and iterates of mean-type mappings
Invariant means and iterates of mean-type mappings Open
Classical result states that for two continuous and strict means $M,\,N \colon I^2 \to I$ ($I$ is an interval) there exists a unique $(M,N)$-invariant mean $K \colon I^2 \to I$, i.e. such a mean that $K \circ (M,N)=K$ and, moreover, the se…
View article: A new invariance identity and means
A new invariance identity and means Open
The invariance identity involving three operations $D_{f,g}:X\times X\rightarrow X$ of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\left( x\right) \oplus g\left( y\right) \right) \text{,} \end{e…
View article: On the special form of integral convolution type inequality due to Walter and Weckesser
On the special form of integral convolution type inequality due to Walter and Weckesser Open
Walter and Weckesser’s result (Aequationes Math 46:212–219, 1993), extending the Bushell–Okrasiński convolution type inequality (Bushell and Okrasiński in J Lond Math Soc (2) 41:503–510, 1990), gave some general conditions on the functions…
View article: Beta-type functions and the harmonic mean
Beta-type functions and the harmonic mean Open
For arbitrary $$f:\left( a,\infty \right) \rightarrow \left( 0,\infty \right) ,$$ $$a\ge 0,$$ the bivariable function $$B_{f}:\left( a,\infty \right) ^{2}\rightarrow \left( 0,\infty \right) ,$$ related to the Euler Beta function, is consid…