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Gyula Maksa

Publications and source records attributed to Gyula Maksa.

5 recordsLinked to original sources
arXiv2015

Convexity with respect to families of means

In this paper we investigate continuity properties of functions $f:\mathbb{R}_+\to\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\big(H_p(x,y)\big)\leq H_q(f(x),f(y)) \qquad(x,y>0), $$ where $H_p$ stands for the $p$th power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are $(p,p)$-Jensen convex for all positive rational number $p$. A counterpart of this result states that if $f$ is $(p,p)$-Jensen convex for all $p\in P\subseteq\mathbb{R}_+$, where $P$ is a set of positive Lebesgue measure, then $f$ must be continuous.

math.CA↗
arXiv2013

A characterization of the relative entropies

In this note we give a characterization of a family of relative entropies on open domain depending on a real parameter $α$ based on recursivity and symmetry. In the cases $α=1$ and $α=0$ we use additionally a weak regularity assumption while in the other cases no regularity assumptions are made at all.

math.CA↗
arXiv2013

Stability of the parametric fundamental equation of information for nonpositive parameters

In this note we prove that the parametric fundamental equation of information is stable in the sense of Hyers and Ulam provided that the parameter is nonpositive. We also prove, as a corollary, that the system of equations that defines the recursive and semi-symmetric information measures depending on a nonpositive parameter is stable in a certain sense.

math.CA↗
arXiv2012

Wigner's theorem revisited

In this paper, we give the general solution of the functional equation $$\big\{\|f(x)+f(y)\|,\|f(x)-f(y)\|\big\}=\big\{\|x+y\|,\|x-y\|\big\}\qquad(x,y\in X)$$ where $f:X\to Y$ and $X,Y$ are inner product spaces. Related equations are also considered. Our main tool is a real version of Wigner's unitary--antiunitary theorem.

math.CA↗