Abstract
The purpose of this paper is to investigate some new dynamic inequalities on time scales. We establish some new dynamic inequalities; the results unify and extend some continuous inequalities and their corresponding discrete analogues. The inequalities given here can be used as tools in the qualitative theory of certain dynamic equations. Some examples are given in the end of this paper.
Highlights
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
Many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales
We investigate some nonlinear integral inequalities on time scales, which extend some inequalities established by Li and Sheng 8 and Li 9
Summary
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. Many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. We investigate some nonlinear integral inequalities on time scales, which extend some inequalities established by Li and Sheng 8 and Li 9. The obtained inequalities can be used as important tools in the study of dynamic equations on time scales. Throughout this paper, let us assume that we have already acquired the knowledge of time scales and time scales notation; for an excellent introduction to the calculus on time scales, we refer the reader to Bohner and Peterson 4 for general overview
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