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In this paper we present a new criterion on characterization of real inner product spaces.
On the ordered sets in n-dimensional real inner product spaces
Real inner product space Lorentz-Minkowski distance Lorentz trans-formation
2008/12/26
Let X be a real inner product space of dimension ¸ 2. In [2],
W. Benz proved the following theorem for x; y 2 X with x < y: "The
Lorentz-Minkowski distance between x and y is zero (i.e., l (x;...
A Potpourri of Schwarz Related Inequalities in Inner Product Spaces (I)
Schwarz's inequality Triangle inequality Inner product spaces
2008/7/3
In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.
A Potpourri of Schwarz Related Inequalities in Inner Product Spaces (II)
Schwarz inequality Inner product spaces Reverse inequalities
2008/7/3
Further inequalities related to the Schwarz inequality in real or complex inner product spaces are given.
A Grüss type inequality for sequences of vectors in inner product spaces and applications
Grüss Inequality inner product spaces
2008/7/3
A Grüss type inequality for sequences of vectors in inner product spaces which complement a recent result from [6] and applications for differentiable convex functions defined on inner product spaces ...
An Identity In Real Inner Product Spaces
Real inner product spaces Equality Grüss inequality
2008/7/2
We obtain an identity in real inner product spaces that leads to the Grüss inequality and an inequality of Ostrowski.
Refinements of Reverse Triangle Inequalities in Inner Product Spaces
Triangle inequality Reverse inequality Diaz-Metkalf inequality Inner product space
2008/6/27
Refining some results of S.S. Dragomir, several new reverses of the triangle inequality in inner product spaces are obtained.
Reverses of Schwarz's Triangle and Bessel Inequalities in Inner Product Spaces
Schwarz's inequality Triangle inequality Bessel's inequality Gruss type inequalities Integral inequalities
2008/6/27
Reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces that produce some earlier results are pointed out. They are applied to obtain new Gruss type inequalities. Some natura...
Some Grüss Type Inequalities in Inner Product Spaces
Grüss' Inequality Inner products Integral inequalities Discrete Inequalities
2008/6/27
Some new Grüss type inequalities in inner product spaces and applications for integrals are given.
The Hypo-Euclidean Norm of an $n-$tuple of Vectors in Inner Product Spaces and Applications
Inner product spaces Norms Bessel's inequality Boas-Bellman and Bombieri inequalities Bounded linear operators Numerical radius
2008/6/26
The concept of hypo-Euclidean norm for an n-tuple of vectors in inner product spaces is introduced. Its fundamental properties are established. Upper bounds via the Boas-Bellman [1]-[3] and Bombieri [...
Some Boas-Bellman Type Inequalities in 2-Inner Product Spaces
Bessel's inequality in 2-Inner Product Spaces Boas-Bellman type inequalities 2-Inner Products 2-Norms
2008/6/26
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral i...
Some Companions of the Grüss Inequality in Inner Product Spaces
Grüss inequality Inner products Integral inequality Inequalities for sums
2008/6/26
Some companions of Grüss inequality in inner product spaces and applications for integrals are given.