INTRODUCTION

1. Introduction

2. Refinements of Young's inequality for two numbers

3. Further generalizations and applications of Young's inequality

4. Classical and abstract mean values
4.1. Gini and Lehmer means
4.2. Quasi-arithmetic means
4.3. Iterative means
4.4. Complete description of mean and entropy functions for two variables

5. Generalizations of discrete Cauchy-Bunyakovsky inequalities
5.1. Historical information
5.2. Milne and Kolboe inequalities
5.3. Daykin-Eliezer-Carlitz theorem

6. Generalizations of integral Cauchy-Bunyakovsky inequalities
6.1. Generalizations with different means
6.2. Generalizations with logarithmic derivatives
6.3. Basic theorems on generalization of integral Cauchy-Bunyakovsky inequality
6.4. Comparison of generalizations of integral Cauchy-Bunyakovsky inequality

7. Applications of generalizations of discrete Cauchy-Bunyakovsky inequalities
7.1. Cauchy-Bunyakovsky inequalities in Lorentz spaces
7.2. Uncertainty principle for DFT

8. Applications of generalizations of integral Cauchy-Bunyakovsky inequalities