Quadratic Reverses of the Triangle Inequality in Inner Product Spaces
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
math.FA↗
arXiv subjects
Sever Silvestru Dragomir
Publications and source records attributed to Sever Silvestru Dragomir.
Some Reverses of the Generalised Triangle Inequality in Complex Inner Product Spaces
Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given.
math.FA↗
A General Divergence Measure for Monotonic Functions and Applications in Information Theory
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
math.PR↗
Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces
The main aim of this monograph is to survey some recent results obtained by the author related to reverses of the Schwarz, triangle and Bessel inequalities. Some Gruss' type inequalities for orthonormal families of vectors in real or complex inner product spaces are presented as well. Generalizations of the Boas-Bellman, Bombieri, Selberg, Heilbronn and Pecaric inequalities for finite sequences of vectors that are not necessarily orthogonal are also provided. Two extensions of the celebrated Ostrowski's inequalities for sequences or real numbers and the generalization of Wagner's inequality in inner product spaces are pointed out. Finally, some Gruss type inequalities for n-tuples of vectors in inner product spaces and their natural applications for the approximation of the discrete Fourier and Mellin transforms are given as well.
math.FA↗
Representation of multivariate functions via the potential theory
In this paper, by the use of Potential Theory, some representation results for multivariate functions from the Sobolev spaces in terms of the double layer potential and the fundamental solution of Laplace's equation are pointed out. Applications for multivariate inequalities of Ostrowski type are also provided.
math.AP↗
On the Chebyshev's Inequality for Weighted Means
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
math.CA↗
Reverses of the Cauchy-Bunyakovsky-Schwarz Inequality for n-tuples of Complex Numbers
Some new reverses of the Cauchy-Bunyakovsky-Schwarz inequality for n-tuples of real and complex numbers related to Cassels and Shisha-Mond results are given.
math.CA↗
Bounding the Chebychev Functional for a Pair of Sequences in Inner Product Spaces
Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.
math.CA↗
New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss type inequalities. Finally, some natural integral inequalities are stated as well.
math.FA↗
Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for integral inequalities are also pointed out.
math.FA↗
On the Bombieri Inequality in Inner Product Spaces
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
math.CA↗
Bounding the Cebysev Functional for Sequences of Vectors in Normed Linear Spaces
Some new bounds for Cebysev functional for sequences of vectors in normed linear spaces are pointed out.
math.CA↗
On Pecaric's Inequality in Inner Product Spaces
Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.
math.AP↗
Some Bombieri Type Inequalities in Inner Product
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
math.CA↗
On the Boas-Bellman Inequality in Inner Product Spaces
New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.
math.CA↗
A Generalisation of the Cassels and Greub-Reinboldt Inequalities in Inner Product Spaces
A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.
math.CA↗
Gruss Type Discrete Inequalities in Normed Linear Spaces, Revisited
Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed spaces are provided as well.
math.CA↗
Gruss Type Discrete Inequalities in Inner Product Spaces, Revisited
Some sharp inequalities of Gruss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided.
math.CA↗