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{\large\sc Numbers, Functions, Equations 2018}\\[1mm]
{\bf Hajd\'uszoboszl\'o (Hungary), August 26 -- September 1, 2018}
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with #5)}\end{center}\vspace{7mm} #6} 

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\abstract
{Bessenyei} % Family name
{Mih\'aly} % First name
{University of Debrecen, Debrecen} % Affiliation
{Generalized monotonicity in terms of differential inequalities} % Title of talk
{} % Coauthor(s)
{The notions of monotonicity and convexity can be characterized via
the nonnegativity of the first and the second derivative, respectively. These classical notions can
be extended applying Chebyshev systems \cite{KarStu66}. The main result of the talk \cite{Bes18},
analogously to the classical derivative tests, characterizes generalized monotonicity in terms of
differential inequalities. Applications in the fields of convexity and ordinary differential equations
are also discussed. The key tool of the approach is the P\'ales mean-value theorem \cite{Pal16}.}

\begin{thebibliography}{22}
  
\bibitem{Bes18}
  M.~Bessenyei, \emph{Generalized monotonicity in terms of differential inequalities},
  Proc. Roy. Soc. Edinburgh Sect. A  (2018), to appear.

\bibitem{KarStu66}
  S.~Karlin and W.~J. Studden, \emph{Tchebycheff systems: {W}ith applications in analysis and statistics},
  Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley \& Sons, New York-London-Sydney, 1966.
  
\bibitem{Pal16}
  Zs.~P\'ales, \emph{A general mean value theorem},
  Publ. Math. Debrecen, \textbf{89} (2016), no.~1-2, 161--172.
 
\end{thebibliography}

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