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SOME NEW RESULTS RELATED TO BESSEL AND GRUSS INEQUALITIES IN 2-INNER PRODUCT SPACES AND APPLICATIONS

  • DRAGOMIR S.S. ;
  • CHO, Y.J. ;
  • KIM, S.S.
  • Published : 2005.08.01

Abstract

Some new reverses of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces are pointed out. Applications for some Gruss type inequalities and for determinantal integral inequalities are given as well.

Keywords

Bessel's inequality;Gruss' inequality;2-inner product;Lebesgue integral;synchronous functions

References

  1. Y. J. Cho, Paul C. S. Lin, S. S. Kim, and A. Misiak, Theory of 2-inner product spaces, Nova Science Publishers, Inc., New York, 2001
  2. Y. J. Cho, M. Matic, and J. E. Pecaric, On Gram's determinant in 2-inner product spaces, J. Korean Math. Soc. 38 (2001), no. 6, 1125-1156
  3. S. S. Dragomir, Y. J. Cho, S. S. Kim, and Y.-H. Kim, On Bessel's and Gruss' inequalities for orthonormal families in 2-inner product spaces and applications, Preprint on line: http://www.mathpreprints.com/math/Preprint/Sever/20030929/1/
  4. S. S. Dragomir, Y. J. Cho, S. S. Kim, and J. Roumeliotis, A reverse of Bessel's inequality in 2-inner product spaces and some Gruss type related results with applications, preprint on line: http://www.mathpreprints.com/math/Preprint/Sever/20030923.1/2
  5. R. W. Freese and Y. J. Cho, Geometry of linear 2-normed spaces, Nova Science Publishers, Inc., New York, 2001

Cited by

  1. More results on a functional generalization of the Cauchy-Schwarz inequality vol.2012, pp.1, 2012, https://doi.org/10.1186/1029-242X-2012-239