Some Reverses Of The Cauchy Bunyakovsky Schwarz Inequality In 2 Inner Product Spaces
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Some Reverses of the Cauchy-Bunyakovsky-Schwarz Inequality in 2-Inner Product Spaces
In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.
Advances in Inequalities of the Schwarz, Grüss, and Bessel Type in Inner Product Spaces
Author: Sever Silvestru Dragomir
language: en
Publisher: Nova Publishers
Release Date: 2005
The theory of Hilbert spaces plays a central role in contemporary mathematics with numerous applications for Linear Operators, Partial Differential Equations, in Nonlinear Analysis, Approximation Theory, Optimisation Theory, Numerical Analysis, Probability Theory, Statistics and other fields. The Schwarz, triangle, Bessel, Gram and most recently, Grüss type inequalities have been frequently used as powerful tools in obtaining bounds or estimating the errors for various approximation formulae occurring in the domains mentioned above. Therefore, any new advancement related to these fundamental facts will have a flow of important consequences in the mathematical fields where these inequalities have been used before.
Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals
Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2--inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.