Abstract
The objective of this paper is to study some dynamic integral inequalities on time scales, which provide explicit bounds on unknown functions. Our results include many known ones in the literature and can be used as tools in the study of qualitative theory of certain classes of dynamic equations with mixed nonlinearities on time scales.
Highlights
The theory of time scales was introduced and developed by Hilger [ ] and Bohner and Peterson [, ] in order to unify continuous and discrete analysis
It has been applied to various fields of mathematics
Many authors have extended some integral inequalities used in the theory of differential, difference, and integral equations to an arbitrary time scale; see, for instance, the papers [ – ] and the references cited therein
Summary
The theory of time scales was introduced and developed by Hilger [ ] and Bohner and Peterson [ , ] in order to unify continuous and discrete analysis. ] Assume that u, a, b, f , g : Tk → R+ are rd-continuous functions and let p and q be real constants satisfying p ≥ q > .
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