Generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function

Abstract

Abstract. We prove generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalities.Mathematics subject classification (2010): 26D10, 26D15, 26E70.

Generalized Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

“…Liu et al [24] obtained the following generalization of the Montgomery identity on time scales (2): Theorem 4. Let α, β, η, τ ∈ T, with α < β and φ : [α, β] T → R be a delta differentiable function.…”

“…Some various generalizations and extensions of the dynamic Ostrowski inequality can be found in the papers [34,33,5,18,50,24,32,37,45,47,48,43,42,41].…”

“…Also in [24], the authors generalized the dynamic Ostrowski inequality (2) by using the generalized Montgomery identity on time scales (4). Their result can be stated as…”

A Parameter-Based Ostrowski–Grüss Type Inequalities with Multiple Points for Derivatives Bounded by Functions on Time Scales

“…Several other inequalities could be obtained by choosing different time scales with different values of the parameter λ. Some related results on the Ostrowski-type inequalities can be found in [25][26][27][28][29][30][31][32][33][34][35].…”

New Ostrowski and Ostrowski-Gruss type inequalities for double integrals on time scales involving a combination of $\Delta$-integral means

“…Over the years many authors have studied different generalizations of Theorem 2 for functions of a single variable (see [13,17,18,19,23] and the references therein) as well as for functions of two independent variables (see [10,11,15,16,21,22] and the references therein).…”