Continuous Versions of Some Classical Inequalities

著者名：Nikolova, Ludmila/Persson, Lars-Erik/Varošanec, Sanja

Birkhäuser（2025/04/26発売）

• 言語：ENG
• ISBN：9783031833717
• eISBN：9783031833724

Description

This book presents the new fascinating area of continuous inequalities. It was recently discovered that several of the classical inequalities can be generalized and given in a more general continuous/family form. The book states, proves and discusses a number of classical inequalities in such continuous/family forms. Moreover, since many of the classical inequalities hold also in a refined form, it is shown that such refinements can be proven in the more general continuous/family frame.

Written in a pedagogical and reader-friendly way, the book gives clear explanations and examples on how this technique works. The presented interplay between classical theory of inequalities and these newer continuous/family forms, including some corresponding open questions, will appeal to a broad audience of mathematicians and serve as a source of inspiration for further research.

Table of Contents

- 1. Continuous Forms of Classical Inequalities.- 2. Refinements of Continuous Forms of Inequalities.- 3. Refinements of Inequalities via Strong Convexity and Superquadracity.- 4. Functionals Associated with Continuous Forms of Inequalities.- 5. Some Classical Inequalities Involving Banach Lattice Norms.