6 papers
Equality problem for generalized quasiarithmetic means generated by discontinuous strictly monotonic functions
Tibor Kiss, PaweÅ 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…
Strictly nonexpansive, strictly monotone quasi graph-additive functions
Tibor Kiss
In this paper, we provide a negative answer to an open problem concerning the functional equation \[f(f(-x)+x)=f(-f(x))+f(x),\] namely by showing that the family of continuous solu…
Lattice-like property of quasi-arithmetic means: revisited
Tibor Kiss, PaweÅ Pasteczka
We show that every family of quasi-arithmetic means generated by (a subset of) functions with nonvanishing derivative which is bounded (from below or from above) by…
Non-symmetrically -affine functions revisited
Tibor Kiss, Dóra Koroknai
In 2014, Michal Lewicki and Andrzej OlbryÅ proved that if a real valued function defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f…
Improved regularity for a composite functional equation stemming from the theory of means
Tibor Kiss, Péter Tóth
In this paper we describe the solutions of the functional equation \begin{equation*} F\Big(\frac{x+y}2\Big)+f_1(x)+f_2(y)=G \big(g_1(x)+g_2(y)) \end{equation*} defined on an open s…
On the -balancing property of multivariate generalized quasi-arithmetic means
Tibor Kiss, GergÅ Nagy
The aim of this paper is to characterize the so-called -balancing property in the class of generalized quasi-arithmetic means. In general, the question is whether those element…