Some Iyengar-type inequalities on time scales for functions whose second derivatives are bounded

Some New Gronwall-Bellman-Type Inequalities on Time Scales and Their Applications

“…During the past decades, many Gronwall-Bellman-type inequalities have been discovered (e.g., see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). Recently, with the development of the theory of time scales [19], many integral inequalities on time scales have been established, for example, [20][21][22][23][24][25][26][27][28][29][30][31][32], which have proved to be very effective in the analysis of qualitative as well as quantitative analysis of solutions of dynamic equations. But for some certain dynamic equations, for example,…”

Some Delay Integral Inequalities on Time Scales and Their Applications in the Theory of Dynamic Equations

“…On the other hand, Hilger 14 initiated the theory of time scales as a theory capable to contain both difference and differential calculus in a consistent way. Since then many authors have expounded on various aspects of the theory of dynamic equations on time scales including various inequalities on time scales e.g., see [15][16][17][18][19][20][21][22][23][24] , and the references therein . However, delay integral inequalities on time scales have been paid little attention so far.…”

Explicit Bounds to Some New Gronwall‐Bellman‐Type Delay Integral Inequalities in Two Independent Variables on Time Scales

“…Since then many authors have expounded on various aspects of the theory of dynamic equations on time scales e.g., see 15-17 and the references therein . In these investigations, integral inequalities on time scales have been paid much attention by many authors, and a lot of integral inequalities on time scales have been established e.g., see [18][19][20][21][22][23][24][25][26] , which have been designed to unify continuous and discrete analysis and play an important role in the research of qualitative and quantitative properties of solutions of certain dynamic equations on time scales. But to our knowledge, Gronwall-Bellman-type delay integral inequalities on time scales have been paid little attention in the literature so far.…”