ON THE PARALLELOGRAM LAW AND BOHR'S INEQUALITY IN G-INNER PRODUCT SPACES

  • Cho, Yeol-Je (Department of Mathematics Education and the RINS, College of Education, Gyeongsang National university) ;
  • Culjak, Vera (Department of Mathematics, Faculty of Civil Engineering, University of Zagreb) ;
  • Pecaric, Josip (Faculty of Textile Technology, Univeristy of Zagreb)
  • Published : 2009.02.28

Abstract

In this paper, we give some results which are in connection to the parallelogram law in G-inner product spaces and also prove some results related to Bohr's inequality in G-inner product spaces.

Keywords

References

  1. Y.J. Cho, Paul C.S. Lin, S.S. Kim & A. Misiak : Theory of 2-Inner Product Spaces, Nova Science Publishers, Inc., New York, 2001.
  2. Th.M. Rassias : New characterizations of inner product spaces. Bull. Sci. Math. 108(2) (1984), 95-99.
  3. S.S. Dragomir & I. Sandor: Some inequalities in prehilbertian spaces. Studia Univ Babes-Bolyai, Math. 32 (1987), 71-78.
  4. D.S. Mitrinovic, J .E. Pecarie & A.M. Fink: Classical and New Inequalities in Analysis. Kulwer Academic Publishers, 1993.
  5. M.S. Klamkin: A vector norm inequality. Amer. Math. Monthly 82 (1975), 829-830. https://doi.org/10.2307/2319802
  6. T.R Shore: On an inequality of van der Corput and Beth. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 678-715 (1982), 56-57.
  7. J.E. Pecaric & R.R. Janic: Note on a vector norm inequality. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 735-762 (1982), 35-38.
  8. H. Bohr: Zur Theorie der fastperiodischen Funktionen I. Acta Math. 45 (1924), 29-127. https://doi.org/10.1007/BF02395468
  9. J.E. Pecaric & R.R. Janic: Some remarks on the paper "Sur une inegalite de la norm" of D. Dellbosco. Facta Univ. (Nis), Ser. Math. Inform. 3 (1988), 39-42.
  10. J .E. Pecaric & Th.M. Rassias: Variations and generalizations of Bohr's inequality. J. Math. Anal. Appl. 178 (1993), 138-146.
  11. Th.M. Rassias: On characteraziations of inner product spaces and generalizations of zhe H. Bohr inequality. in: "Topics in Mathematical Analysis" (ed. Th.M. Rassias), Singapore, 1989.
  12. D. Delbosco: Sur une inegalite de la norm. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 678-715 (1980), 206-208.
  13. V.L. Kocic & D.M. Maksimovic: Variations and generalizations of an inequality due to Bohr. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 412-460 (1973), 183-188.
  14. J.E. Pecarie & S.S. Dragomir: A refinement of Jensen inequality and applications. Babes-Bolyai, Mathematica 34 (1989), 15-19.
  15. H. Bergstrom: A triangle-inequality for matrices. Den 11-te Skandinaviske Mathematikerkongress. Trondheim 1949, Oslo, 1952, 264-267.
  16. Y.J. Cho, M. Matic & J. Pecaric: Inequalities of Hlawka's type in G-inner product spaces. Inequality Theory and Applications, Vol. 1., Nova Science Publishers, Inc., New York, 2001.