An Ostrowski–Grüss type inequality on time scales

Abstract

a b s t r a c tWe derive a new inequality of Ostrowski-Grüss type on time scales by using the Grüss inequality on time scales and thus unify corresponding continuous and discrete versions. We also apply our result to the quantum calculus case.

Ostrowski Type Inequalities on Time Scales for Double Integrals

“…Since then, many authors have studied certain integral inequalities or dynamic equations on time scales [1,7,8,16,[28][29][30][31]36]. In [8], Bohner and Matthews established the following so-called Ostrowski inequality on time scales which was later generalized by the present authors [18][19][20]23].…”

Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables

“…In recent years, various generalizations of the Ostrowski inequality including continuous and discrete versions have been established (for example, see [3][4][5][6][7][8][9][10][11][12][13][14] and the references therein). On the other hand, Hilger [15] initiated the theory of time scales as a theory capable of treating continuous and discrete analysis in a consistent way, based on which some authors have studied the Ostrowski type inequalities on time scales (see [16][17][18][19][20][21][22][23][24]). The established Ostrowski type inequalities on time scales unify continuous and discrete analysis, and can be used to provide explicit error bounds for some known and some new numerical quadrature formulae.…”

Generalization of Ostrowski and Ostrowski–Grüss type inequalities on time scales

“…Additionally, Liu et al [8] have extended a generalization of an Ostrowski type inequality with a parameter on time scales and a unified corresponding continuous and discrete case.…”