Dynamic inequalities of Grüss, Ostrowski and Trapezoid type via diamond-$ \alpha $ integrals and Montgomery identity

Abstract

<abstract><p>In this article, the Montgomery identity and Ostrowski inequality are established for univariate first-order diamond-alpha differentiable functions. We also investigate the generalization of Ostrowski-type inequalities for bivariate functions with bounded second-order diamond-alpha derivatives by applying integration by parts for $ \diamondsuit_\alpha $-integrals. Moreover, some extensions of dynamic trapezoid- and Grüss-type inequalities are also obtained by using the Montgomery identity.</p></abstract>