ABSTRACT
The Jensen inequality is the most important. With more or less effort, almost all important and influential inequalities can be derived from Jensen’s. Discrete form of Jensen’s inequality includes a real vector space, convex combination with its center, and convex function. The Hermite-Hadamard inequality is the double inequality with harmonic form consisting of the integral member between two discrete members. The Rogers-Holder inequality occupies an important place in mathematical analysis, especially in the study and development of Lp spaces. Although it comes down to nonnegative real-valued functions, complex-valued functions are used due to their wider applications. The integral form of the Rogers-Holder inequality can be transformed into discrete form by taking advantage of the counting measure. The Minkowski inequality is the key inequality of functional analysis. It has the greatest influence in the normed vector spaces.
