Formation of versions of some dynamic inequalities unified on time scale calculus

The aim of this paper is to present some comprehensive and extended versions of classical inequalities such as Radon’s Inequality, Bergstrom’s Inequality, the weighted power mean inequality, Schlomilch’s Inequality and Nesbitt’s Inequality on time scale calculus. In time scale calculus, results are unified and extended. The theory of time scale calculus is applied to unify discrete and continuous analysis and to combine them in one comprehensive form. This hybrid theory is also widely applied on dynamic inequalities. The study of dynamic inequalities has received a lot of attention in the literature and has become a major field in pure and applied mathematics.