Dynamic Inequalities On Time Scales

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

“…Inspired by the ideas employed in [17,19], here we obtain generalized Ostrowski and Ostrowski-Grüss inequalities on time scales via a parameter function. Our results are different from the ones given in [17] since we are using the generalized weighted Peano kernel (1). Furthermore, we apply our result to the continuous, discrete, and quantum cases, to obtain some interesting new inequalities.…”

“…For the proof of our main results (Theorems 16 and 24), we use the following useful lemma. 1]. Then the following equality holds:…”

“…THEOREM 24. Let ν : [a, b] → [0, ∞) be rd -continuous and positive, and func- 1]. Then, the inequality…”

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

“…The books on the subject of time scales by Bohner and Peterson [10] summarize and organize much of time scale calculus. During the past decade a number of dynamic inequalities has been established by some authors which are motivated by some applications (see [1,7,8,21,27,13,22,25,26,40,9,4,46,2,49]). …”

Some reverse Hölder inequalities with Specht's ratio on time scales

“…The book on the subject of time scales by Bohner and Peterson [6] summarizes and organizes much of time scale calculus. During the past decade a number of dynamic inequalities has been established by some authors which are motivated by practical problems, for example, when studying the behavior of solutions of certain class of dynamic equations on a time scale T, see [2,3,6], and the references cited therein.…”