Some Integral Inequalities on Time Scales

Some New Integral Inequalities on Time Scales

By introducing two adjusting parameters, we investigate some new nonlinear integral inequalities on time scales, which provide explicit bounds on unknown functions, and can be used as tools in the qualitative theory of certain classes of dynamic equations on time scales. Mathematics subject classification (2010): 26D15, 26E70.

On Some Nonlinear Integral Inequalities on Time Scales

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

On Some Integral Inequalities on Time Scales and Their Applications

The theory of time scales was introduced by Hilger 1 in 1988 in order to contain both difference and differential calculus in a consistent way. Recently, many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. For example, we refer the reader to the papers 2–12 and the references cited there in. In this paper, w...

Research Article Some Nonlinear Integral Inequalities on Time Scales

The theory of time scales was introduced by Hilger [1] in his Ph.D. thesis in 1988 in order to unify continuous and discrete analysis. Recently, many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. For example, we refer the reader to the literatures [2–8] and the references cited therein. In this paper, we in...

Some nonlinear dynamic integral inequalities on time scales