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Dynamic inequalities of Grüss, Ostrowski and Trapezoid type via diamond-$ \alpha $ integrals and Montgomery identity
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<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 $-integrals. Moreover, some extensions of dynamic trapezoid- and Grüss-type inequalities are also obtained by using the Montgomery identity.</p></abstract>
American Institute of Mathematical Sciences (AIMS)
Title: Dynamic inequalities of Grüss, Ostrowski and Trapezoid type via diamond-$ \alpha $ integrals and Montgomery identity
Description:
<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>.
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On Dynamic Inequalities of Grüss, Ostrowski and Trapezoidal Type via Nabla‐
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