Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Bessel's and Grüss Inequalities for Orthonormal Families in 2-Inner Product Spaces and Applications

  • Dragomir, Sever Silverstru (School of Computer Science and Mathematics, Victoria University of Technology) ;
  • Cho, Yeol-Je (Department of Mathematics Education, The Research Institute of Natural Sciences, Gyeongsang National University) ;
  • Kim, Seong-Sik (Department of Mathematics, Dongeui University) ;
  • Kim, Young-Ho (Department of Applied Mathematics, Changwon National University)
  • Received : 2005.04.15
  • Published : 2008.06.30
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Abstract

A new counterpart of Bessel's inequality for orthonormal families in real or complex 2-inner product spaces is obtained. Applications for some Gr$\"{u}$ss inequality for determinantal integral inequalities are also provided.

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References

  1. Y. J. Cho, 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 Grams determinant in 2-inner product spaces, J. Korean Math. Soc., 38(6)(2001), pp. 1125-1156.
  3. 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 Gr¨uss type related results with applications, J. Appl. Math. & Computing, 20(1-2)(2006), pp. 279-292. https://doi.org/10.1007/BF02831938
  4. D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, 1993.
  5. R. W. Freese and Y. J. Cho, Geometry of Linear 2-Normed Spaces, Nova Science Publishers, Inc., New York, 2001.