Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces

By Sever Silvestru Dragomir. 2003

97 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2e342f6cb5892255c812df31dcbe41c756400ea4

Citations in the corpus

• New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces (2008, unknown): “Finally, another inequality of Gr¨uss’ type that has been obtained in [ 8 ] (see also [ 10 , p. 65]) can be stated as:”