A new look at classical inequalities involving Banach lattice norms

Journal of inequalities and applications

Ludmila Nikolova¹ 

关键词: inequalities;    continuous forms;    Hölder’s inequality;    Minkowski’s inequality;    Popoviciu’s inequality;    Bellman’s inequality;    Beckenbach-Dresher’s inequality;    Milne’s inequality;    Banach function space;    interpolation of families of spaces;    26D10;    26D15;    46B70;    46E15;   

DOI  :  10.1186/s13660-017-1576-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of this type and also by deriving some new results related to classical Popoviciu’s, Bellman’s and Beckenbach-Dresher’s inequalities.

【 授权许可】

CC BY