Inequalities lie at the heart of the mathematical analysis which is a major and important branch of mathematics. Throughout the history, many researchers discovered agreat number of inequalities that are very useful in many fields of mathematics. Thestudy of inequalities became very popular in the twentieth century specially afterthe publishing of the pioneering book. In 1988, Stephan Hilger introduced in his PhD thesis a new theory, the theoryof time scales, which builds bridges between continuous and discrete mathematics.The main idea is to prove a result for a dynamic inequality where the...