Functional inequalities in the framework of Banach spaces
Functional Analysis
2024-08-16 v2 Classical Analysis and ODEs
Abstract
A quadrilateral inequality established by C. Sch\"otz in the context of Hilbert spaces is extended to the framework of Banach spaces. Our approach is based on the majorization theory and a substitute for the parallelogram law associated with Clarkson's notion of von Neumann-Jordan constant. As a by-product, several functional inequalities that extend classical inequalities from linear algebra and geometry of Banach spaces are also obtained.
Keywords
Cite
@article{arxiv.2405.20097,
title = {Functional inequalities in the framework of Banach spaces},
author = {Constantin P. Niculescu},
journal= {arXiv preprint arXiv:2405.20097},
year = {2024}
}
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19 pages