SOME GENERALIZED OSTROWSKI- AND OSTROWSKI-GRÜSS-TYPE INEQUALITIES ON FRACTAL SETS AND THEIR APPLICATIONS

Abstract

We establish new inequalities of generalized Ostrowski- and Ostrowski–Grüss-type on fractal sets. They depend on a new generalized Montgomery identity on fractal sets and a parameter function $h:[0,1]\to [0,1]$. Our results not only give an error estimate for $\frac{\mathrm{\Gamma }(1+\alpha )}{{(b-a)}^{\alpha }}{}_a{I}_b^{\alpha }f(t)$ with $f(x)$, $f(a)$ and $f(b)$, but also generalize and extend previous results of Sarikaya, Budak and coauthors. We give applications to two-point and three-point quadrature formulas.