Some nonlinear dynamic inequalities on time scales

Abstract

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736-751).

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]). …”

Certain Nonlinear Integral Inequalities and Their Applications

“…It is well known that integral inequalities are very useful to investigate the existence, uniqueness, boundedness, oscillation, and other qualitative properties of solutions to differential equations and integrodifferential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. One of the fundamental inequalities is the Gronwall inequality, which was established in 1919 by Gronwall [1].…”

Some delay integral inequalities on time scales

“…Since then many authors have expounded on various aspects of the theory of dynamic equations and dynamic inequalities on time scales. For example, see [2][3][4][5][6][7][8][9][10][11][12] and the references therein. However, as far as we know, nobody has studied the delay integral inequalities on time scales.…”