What question did this study set out to answer?

The goal is to establish a new bound for Schwarz's inequality specifically for discrete scenarios.

April 3, 20260 citationsOpen Access

A Converse of Schwarz’s Inequality

Key Points

The goal is to establish a new bound for Schwarz's inequality specifically for discrete scenarios.
Analyzed the properties of Schwarz's inequality in a discrete context.
Utilized biharmonic Green's functions to develop the new bound.
Compared results with established continuous cases.
Provided a precise bound for the discrete case of Schwarz's inequality.
Demonstrated efficacy of biharmonic Green's functions in estimating bounds.

Abstract

A converse of Schwarz's inequality was studied by Bellman 2.He gave an explicit bound for a continuous case.We aim to give a bound of Schwarz's inequality for the discrete case.Our method is to use the ratio of the value of biharmonic Green's functions.

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Cite This Study

倉田 et al. (Wed,) studied this question.

synapsesocial.com/papers/69cf59635a333a821460a0a2 https://doi.org/https://doi.org/10.24568/55451