On some Ostrowski type inequalities via Montgomery identity and Taylor's formula

Abstract

A new extension of the weighted Montgomery identity is given, by using Taylor's formula, and used to obtain some Ostrowski type inequalities and the estimations of the difference of two integral means.

Extension of Montgomery identity via Taylor polynomial on time scales

“…Further, it is applied to find extended form of Ostrowski type inequality, midpoint inequality and trapezoid type inequality on time scales in generalized forms along with the weighted version of obtained Montgomery identity and respective Ostrowski's inequality. As special cases, our inequalities contain the results proved in [4] when T = R . Moreover, our results can be used to prove certain integral inequalities including Čebyšev-Grüss type inequality, Steffensen's inequality and Popoviciu type inequality in more generalized settings, e.g., it is possible to extend the results given in [5,10,20] with the help of new inequalities presented here.…”

“…Use (3.8)-(3.11) in (3.4)-(3.7) respectively to get the desired result. If we use T = R in Theorem 3.1, (3.1) becomes(2.2) in[4].…”

Sharp Integral Inequalities Based on General Two-Point Formulae via an Extension of Montgomery’s Identity

“…In a recent paper [1] the following extension of the Montgomery identity via Taylor's formula has been proved:…”

Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions

“…In the case u(t) = t,t£ [a, b], the above identity reduces to the celebrated Montgomery identity (see [14, p. 565]) that has been extensively used by many authors in obtaining various inequalities of Ostrowski type. For a comprehensive recent collection of works, see the book [12] and the papers [1,2,3,4,5,13,15,19,20]. It has been shown in [9] that, if / : [a, b] -¥ R is a function of bounded variation and u : [a, b) -¥ K is of r-H-Holder type, that is, (1)(2) \u(x) -u(y)\ ^ H \ x -y \ r for a n y x , y e [ a , b ] ,…”