21 citations · 163 across the 30 of their papers we have counts for
30 papers · 1 filter
On approximately convex and affine functions
Angshuman R. Goswami, Zsolt Páles
A real valued function defined on a real open interval is called -convex if, for all , it satisfies $$ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)+tΦ\big((1-t…
Characterizations of the equality of two-variable generalized quasiarithmetic means
Zsolt Páles, Amr Zakaria
This paper is motivated by an astonishing result of H. Alzer and S. Ruscheweyh published in 2001 in the Proc. Amer. Math. Soc., which states that the intersection of the classes tw…
An extension of the Abel-Liouville identity
Zsolt Páles, Amr Zakaria
In this note, we present an extension of the celebrated Abel-Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characteriz…
On the Jensen convex and Jensen concave envelopes of means
Zsolt Páles, Paweł Pasteczka
In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexi…
Characterization of approximately monotone and approximately Hölder functions
Angshuman R. Goswami, Zsolt Páles
A real valued function defined on a real open interval is called -monotone if, for all with it satisfies where $Φ:[0,\el…
On additive functions with additional derivation properties
Richárd Grünwald, Zsolt Páles
The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The bas…
On the equality of two-variable general functional means
László Losonczi, Zsolt Páles, Amr Zakaria
Given two functions and a probability measure on the Borel subsets of , the two-variable mean is defined by $$ M_{f,g;μ}(x,y) :…
Convexity properties of functions defined on metric Abelian groups
Włodzimierz Fechner, Zsolt Páles
The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the struc…
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…
On approximately monotone and approximately Hölder functions
Angshuman R. Goswami, Zsolt Páles
A real valued function defined on a real open interval is called -monotone if, for all with it satisfies where $Φ:[0,\el…
Characterization of the equality of Cauchy means to quasiarithmetic means
Rezső L. Lovas, Zsolt Páles, Amr Zakaria
The main result of this paper provides six necessary and sufficient conditions under various regularity assumptions for a so-called Cauchy mean to be identical to a two-variable qu…
On the equality of Bajraktarević means to quasi-arithmetic means
Zsolt Páles, Amr Zakaria
This paper offers a solution of the functional equation where is a fixed numbe…
On the equality problem of generalized Bajraktarević means
Richárd Grünwald, Zsolt Páles
The purpose of this paper is to investigate the equality problem of generalized Bajraktarević means, i.e., to solve the functional equation \begin{equation}\label{E0}\tag{*} f^{(-1…
On a functional equation related to two-variable Cauchy means
Tibor Kiss, Zsolt Páles
In this paper, we are dealing with the solution of the functional equation concerning the unknown functions and defined…
On Hardy type inequalities for weighted means
Zsolt Páles, Paweł Pasteczka
The aim of this paper is to establish weighted Hardy type inequality in a broad family of means. In other words, for a fixed vector of weights and a weighted m…
On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means
Zsolt Páles, Paweł Pasteczka
The aim of this paper is to characterize the so-called Hardy means, i.e., those means that satisfy the inequality $$ \su…
On a functional equation related to two-variable weighted quasi-arithmetic means
Tibor Kiss, Zsolt Páles
In this paper, we are going to describe the solutions of the functional equation concerning the unknown functions an…
On the local and global comparison of generalized Bajraktarević means
Zsolt Páles, Amr Zakaria
Given two continuous functions such that is positive and is strictly monotone, a measurable space , a measurable family of -variable means…
A new characterization of convexity with respect to Chebyshev systems
Zsolt Páles, Éva Székelyné Radácsi
The notion of th order convexity in the sense of Hopf and Popoviciu is defined via the nonnegativity of the st order divided differences of a given real-valued function.…
Characterization of the Hardy property of means and the best Hardy constants
Zsolt Páles, Paweł Pasteczka
The aim of this paper is to characterize in broad classes of means the so-called Hardy means, i.e., those means that sat…
A General Mean Value Theorem
Zsolt Páles
In this note a general a Cauchy-type mean value theorem for the ratio of functional determinants is offered. It generalizes Cauchy's and Taylor's mean value theorems as well as oth…
Implications between generalized convexity properties of real functions
Tibor Kiss, Zsolt Páles
Motivated by the well-known implications among -convexity properties of real functions, analogous relations among the upper and lower -convexity properties of real functions…