Introduction and Notation

Mathematical inequalities, seeking to set bounds for a mathematical expression, have a long and rich history. Though many of them were explored initially as a mathematical curiosity, they started to be studied subsequently with a rigorous mathematical purpose and intent, and sometimes even motivated by some applied practical problems. Then, the publication of the book Inequalities in 1934, by Hardy, Littlewood and Pólya, resulted in making the study of inequalities into a formal and active area of mathematical research. In the field of Probability and Statistics, various stochastic inequalities were also established, including the celebrated Chebyshev, Markov and Jensen inequalities.