Advances in Mathematical Inequalities and Applications

Dear Colleagues,

Why do we study inequalities? The answer to this question was given by Bellman in a very concrete and elegant fashion: "There are three reasons for the study of inequalities: practical, theoretical and aesthetic. In many practical investigations, it is necessary to bound one quantity by another. The classical inequalities are very useful for this purpose. From the theoretical point of view, very simple questions give rise to entire theories. For example, we may ask when the nonnegativity of one quantity implies that to another. This simple question leads to the theory of positive operators and theory of differential inequalities. Another question which gives rise to much interesting research is that of finding equalities associated with inequalities. We use the principle that every inequality should come from an equality which makes the inequality obvious. Along these lines, we may also look for representation which make inequalities obvious. Often, these representations are maxima or minima of certain quantities. Finally, let us turn to aesthetic aspects. As has been pointed out, beauty is in the eyes of the beholder. However, it is generally agreed that certain pieces of music, art or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive."
In this Special Issue, we present new results related to some classical inequalities such as the Jensen inequality, Jensen–Steffensen inequality, Jessen inequality, Grüss inequality, Chebyshev inequality, etc. They have various applications in other branches of mathematics, such as numerical analysis, probability and statistics, as well as in other sciences such as information theory.

Prof. Dr. Milica Klaricic Bakula
Guest Editor

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