Speaker
Gorana Aras-Gazic
(University of Zagreb Faculty of Architecture)
Description
By utilizing integral arithmetic mean $F$ defined as
$$
F(x,y)=\left\{\begin{array}{cc}
\frac{1}{y-x}\int_{x}^{y}f(t)dt, & x,y\in I,~x\neq y,\\
f(x), & x=y\in I
\end{array}\right.
$$
and applying a generalized form of Niezgoda's inequalty, we present new proofs concerning the $(m,n)$-convexity of the integral arithmetic mean function. This paper aims to contribute novel proofs to D. E. Wulbert's findings, which demonstrate that the integral arithmetic mean exhibits convexity on $I^{2}$ provided $f$ is convex on $I$.
Additionally, we establish an inequality for divided differences by employing the extended form of Niezgoda's inequality. Moreover, we demonstrate the convexity of the function defined by these divided differences.
Primary author
Gorana Aras-Gazic
(University of Zagreb Faculty of Architecture)
Co-authors
Marjan Praljak
(University of Zagreb Faculty of Food Technology and Biotechnology)
Josip Pečarić
(Croatian Academy of Sciences and Arts)
