Speaker
Description
The classical Ostrowski inequality states:
$
\left\vert f(x)-\frac{1}{b-a}\int_{a}^{b}f(t)dt\right\vert \leq\left[
\frac{1}{4}+\frac{\left( x-\frac{a+b}{2}\right) ^{2}}{\left( b-a\right)
^{2}}\right] \left( b-a\right) \left\Vert f^{\prime}\right\Vert _{\infty
},
$
for all $x \in \left[a,b\right]$, where $f:\left[a,b\right]\to \mathbb{R}$ is continuous on $\left[a,b\right]$ and differentiable on $\left( a,b \right)$ with bounded derivative. Ostrowski type inequalities have been largely investigated in the literature since they are very useful in numerical analysis and probability theory.
The main purpose of this talk is to present new Ostrowski type inequalities for $3$-convex functions and for functions whose modulus of derivatives are convex, using the weighted Montgomery identity. We also derive certain Hermite-Hadamard inequalities for $3$-convex functions by applying those results.
