The article explores various classical and new inequalities in analysis, focusing on topics like convex functions, means, determinantal and matrix inequalities, and more. The researchers delve into different types of inequalities and their connections, using methods like dynamic programming and functional equations. Key findings include results such as Jensen's Inequality, Bernoulli's Inequality, and Young's Inequality, among others. The study also discusses applications of inequalities in areas like continued fractions, interpolation, and minimax methods.