A variety of dynamic inequalities on time scales with retardation
Authors
A. A. ElDeeb
 Department of Mathematics, Faculty of Science, AlAzhar University, Nasr City (11884), Cairo, Egypt.
WingSum Cheung
 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong.
Abstract
In this paper, we will prove some new nonlinear retarded dynamic inequalities of GronwallBellman type on time scales. These inequalities are of new forms compared with the existing results so far in the literature, which can be used as effective tools in the study of certain nonlinear retarded dynamic equations. Some special cases of our results contain continuous Gronwalltype inequalities and their discrete analogues. We also indicate some application examples to illustrate our results at the end.
Keywords
 Gronwall's inequality
 Young's inequality
 time scales
MSC
 26A15
 39A12
 34A12
 34A40
 26D10
 26D15
 26D20
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