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

Abstract

In this paper, we prove some new generalizations of dynamic Opial-type inequalities on time scales. From these inequalities, as special cases, we formulate some integral and discrete inequalities proved in the literature and also extend some obtained dynamic inequalities on time scales. The main results are proved by using some algebraic inequalities, Hölder's inequality, and a simple consequence of Keller's chain rule on time scales.

Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform

“…Hilger [2] suggested time scales theory to unify discrete and continuous analysis. More Hilbert-type inequalities and other types can be seen in [1,, see also [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. For more details on time scales calculus see [54].…”

A Variety of Weighted Opial-Type Inequalities with Applications for Dynamic Equations on Time Scales

“…Numerous scholars have been interested in, and are currently interested in, the study of opioid-type inequalities. The Opial Inequalities have undergone various extensions in recent years; for further information, see articles [7][8][9][10][11][12][13][14][15][16][17][18][19][20]). For more details on Opial-type inequalities, see the monograph [21].…”

On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales

“…For more details on Hardy-type inequalities and other types on time scales, we suggest [17][18][19][20][21][22][23][24][25][26][27][28][29] for the reader. ).…”