15 citations · 135 across the 49 of their papers we have counts for
42 papers · 1 filter
Equality problem for generalized quasiarithmetic means generated by discontinuous strictly monotonic functions
Tibor Kiss, Paweł Pasteczka
We study the equality problem of generalized quasiarithmetic means for a strictly monotonic generator that is not necessarily continuous. We provide two sufficient conditions t…
On subadditive quasi-arithmetic means
Zsolt Páles, Paweł Pasteczka
Let be a continuous and strictly monotone function. In the main result of this paper, we show that, for a fixed , the -variable mean…
Hölder- and Minkowski-type inequalities for generalized quasi-arithmetic means
Zsolt Páles, Paweł Pasteczka
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithm…
Equality and comparison of generalized quasiarithmetic means
Zsolt Páles, Paweł Pasteczka
The purpose of this paper is to extend the definition of quasiarithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one.…
On the new smoothness class of means and its impact to mean-type mappings
Paweł Pasteczka
We define so-called residual means, which have a Taylor expansion of the form for some and a single-variab…
Pexider invariance equation for embeddable mean-type mappings
Paweł Pasteczka
We prove that whenever , () are symmetric, continuous means on the interval and () sati…
Extension theorem for simultaneous q-difference equations and some its consequences
Witold Jarczyk, Paweł Pasteczka
Given a set , intervals and , as well as functions with 's running through the…
On the invariance equation for means of generalized power growth
Paweł Pasteczka
We generalize the result of (Witkowski, 2014) which binds orders of homogeneous, symmetric means of power growth that satisfy the inva…
Estimating the Hardy constant of nonconcave homogenus quasideviation means
Zsolt Páles, Paweł Pasteczka
In this paper, we consider homogeneous quasideviation means generated by real functions (defined on ) which are concave around the point and possess certain upper e…
On the Jensen convexity of quasideviation and Bajraktarević means
Zsolt Páles, Paweł Pasteczka
Motivated by the characterization theorem about the Jensen convexity of quasiarithmetic means obtained by the authors in 2021, our main goal is to establish a characterization of t…
Invariance property for extended means
Paweł Pasteczka
e study the properties of the mean-type mappings of the form $${\bf M}(x_1,\dots,x_p):=\big(M_1(x_{α_{1,1}},\dots,x_{α_{1,d_1}}),\dots,M_p(x_{α_{p,1}},\…
On negative results concerning weak-Hardy means
Paweł Pasteczka
We establish the test which allows to show that a mean does not admit a weak-Hardy property. As a result we prove that Hardy and weak-Hardy properties are equivalent in the class o…
Estimating the Hardy constant of nonconcave Gini means
Zsolt Páles, Paweł Pasteczka
The extension of the Hardy-Knopp-Carleman inequality to several classes of means was the subject of numerous papers. In the class of Gini means the Hardy property was characterized…
There is at most one continuous invariant mean
Paweł Pasteczka
We show that, for a (not necessarily continuous) weakly contractive mean-type mapping (where is an interval and ), the function…
On the Hardy property of mixed means
Paweł Pasteczka
Hardy property of means has been extensively studied by Páles and Pasteczka since 2016. The core of this research is based on few of their properties: concavity, symmetry, monotoni…
On the and pointwise divergence of continuous functions
Karol Gryszka, Paweł Pasteczka
For a family of continuous functions ( is a fixed interval) with define a set $$ I_f:=\big\{x \in I \colon \lim_{n…
On the Jensen convex and Jensen concave envelopes of means
Zsolt Páles, Paweł Pasteczka
In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexi…
Invariant means, complementary averages of means, and a characterization of the beta-type means
Janusz Matkowski, Paweł Pasteczka
We prove that whenever the selfmapping , ( and -s are -variable means on the interval ) is invariant with respect to…
Mean-type mappings and invariance principle
Janusz Matkowski, Paweł Pasteczka
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 conside…
On the integral approach to means and their Hardy property
Paweł Pasteczka
The celebrated Hardy inequality can be written in the form $$\int_0^\infty \mathcal{P}_p \big(f|_{[0,x]}\big)dx \le (1-p)^{-1/p} \int_0^\infty f(x)\:dx \qquad \text{ for }p\in(0,1)…
On properties of weighted Hardy constant for means
Paweł Pasteczka
For a given weighted mean defined on a subinterval of and a sequence of weights we define a Hardy constant as th…
New bounds for the ratio of power means
Zsolt Páles, Paweł Pasteczka
We show that for real numbers with , and the related power means , , the inequality $$\frac{\mathscr{P}_p(x)}{\mathscr{P}_q(x)} \le \exp…
On Hardy type inequalities for weighted quasideviation means
Zsolt Páles, Paweł Pasteczka
Using recent results concerning the homogenization and the Hardy property of weighted means, we establish sharp Hardy constants for concave and monotone weighted quasideviation mea…
From the Ingham--Jessen property to mixed-mean inequalities
Jacek Chudziak, Zsolt Páles, Paweł Pasteczka
For every symmetric mean (where an interval) and a nonzero function , defi…