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

Abstract

Abstract. In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

On some generalizations of nonlinear dynamic inequalities on time scales and their applications

“…and (49) Then as in the proof of previous theorem from (46) we see that the inequalities (25) and (26) hold for v 2 . From (50), (26) and the hypothesis (45). By using Lemma…”

“…The book on the subject of time scales by Bohner and Peterson [14] summarizes and organizes much of time scale calculus. During the past decade a number of dynamic inequalities have been established by some authors which are motivated by some applications, for example, when studying the behavior of solutions of certain class of dynamic equations on a time scale T. We refer the reader to [5,8,9,14,16,22,23,24,25,26,35,36,37,38,48,49,50] for contributions, and the references cited therein.…”

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].…”

On some generalizations of dynamic Opial-type inequalities on time scales

“…During the last decade, many inequalities have been studied by different authors (see [1,2,[10][11][12][13][14]26] and the references cited therein).…”