الفهرس 
SummaryOnly 14 pages are availabe for public view
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Abstract
This Ph. D. thesis is mainly devoted to introduce and study some dynamic inequalities related to Hardy’s inequality on time scales and its applications on the second-order half-linear dynamic equations and on the higher integrability theorems. Chapter (1): In this chapter, we give an introduction and overview of the time scale calculus (especially, delta calculus), the classical Hardy’s inequality with some generalizations and its extensions on time scales. Chapter (2): In this chapter, we prove some new dynamic inequalities on time scales which as special cases contain several generalizations of integral and discrete inequalities due to Hardy, Copson, Leindler, Bennett, Pachpatte and Pečarić and Hanjš Chapter (3): First we give a brief introduction to the continuous, discrete and dynamic Hardy’s inequality with weights. Then, we prove some new characterizations of weights u and υ such that the dynamic Hardy inequality holds for two different cases. For applications, we establish some nonoscillation results for a second-order half-linear dynamic equations. Chapter (4): In this chapter, we prove some new characterizations of the weighted functions such that dynamic inequalities involving Hardy-type operators with general kernels holds for two different cases. Chapter (5): In this chapter, we establish some conditions on nonnegative rd-continuous weight functions u(x) and υ(x) which ensure that a reverse dynamic Hardy inequality with kernel holds for the two different cases. Chapter (6): In this chapter, we establish some new reverse dynamic inequalities and use them to prove some higher integrability theorems for decreasing functions on time scales.