A new inequality of Ostrowski–Grüss type and applications to some numerical quadrature rules

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

“…The above inequality is known in the literature as the Ostrowski-Grüss-type inequality. This inequality has been improved (see [2,3]) and generalized (see [4][5][6][7][8]) in several different ways.…”

“…In particular, the authors in [5,6] obtained some Ostrowski-Grüss-type inequalities with the derivatives bounded by functions instead of scalars. Since the introduction of the theory of time scales by the German mathematician Stefan Hilger in his Ph.D thesis [9], several integral inequalities have been extended to time scales by many authors (see [10][11][12]).…”

“…Motivated by the results in [5,6], the goal of this article is to provide some Ostrowski-Grüss-type inequalities on time scales for functions whose derivatives are bounded by functions. Our findings give a broader view of some established published results.…”

A new generalization of the Ostrowski inequality and applications

“…[3,4]. The following theorem [7] is probably the most recent work about finding appropriate bounds for the Chebyshev functional:…”

“…if and only if w > 0. Similarly, to prove (17) one should refer to (8) and then use theorem A and relation (7). Remark 1.…”