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In the present paper, we prove some new reverse type dynamic inequalities on T. Our main inequalities are proved by using the chain rule and Fubini's theorem on time scales T. Our results extend some existing results in the literature. As special cases, we obtain some new discrete inequalities, quantum inequalities and integral inequalities. [ABSTRACT FROM AUTHOR]

In this article, we will prove some new diamond alpha Hilbert-type dynamic inequalities on time scales which are defined as a linear combination of the nabla and delta integrals. These inequalities extend some known dynamic inequalities on time scales, and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proven by using some algebraic inequalities, diamond alpha Hölder inequality, and diamond alpha Jensen's inequality on time scales. [ABSTRACT FROM AUTHOR]

In this article, by using some algebraic inequalities, nabla Hölder inequalities, and nabla Jensen's inequalities on timescales, we proved some new nabla Hilbert-type dynamic inequalities on timescales. These inequalities extend some known dynamic inequalities on timescales and unify some continuous inequalities and their corresponding discrete analogues. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, Hölder inequality, and Jensen's inequality on time scales. [ABSTRACT FROM AUTHOR]