BEST APPROXIMATION SETS IN LINEAR 2-NORMED SPACES

  • Elumalai, S. (Ramanujan Institute for Advanced Study in Mathematics, University of Madras) ;
  • Cho, Y.J. (Department of Mathematics, Gyeongsan National University) ;
  • Kim, S.S (Department of Mathematics Dongeui Univerasity)
  • Published : 1997.07.01

Abstract

In this paper, we give some properties of the sets $D_z(x_o, G)P_{G, z}(x)$. We also provide the relation between $P_{G, z}(x)$ and G$\hat{a}$teaux derivatives.

Keywords

References

  1. Glasnik Mat. v.27 Gateaux dervatives and 2-inner product spaces Y. J. Cho;S. S. Kim
  2. Math. Nachr v.157 Isosceles orthogonal triples in linear 2-normed spaces Y. J. Cho;C. Diminnie;R. Freese;E. Z. Andalafte
  3. Akad Nauk SSSR. v.1 Cebisevskih Mnojestv, Dokladi N. V. Efumov;S. B. Steckin;N. Sovistva
  4. Math. Today v.9 Farthest points on suns S. Elumalai;R. Ravi
  5. Indian J. Math. v.34 Approximation in linear 2-normed spaces S. Elumalai;R. Ravi
  6. Math. Japon. v.40 An extension theorem for bounded linear 2-functionals and applications I. Franic
  7. Math. Nachr. v.105 Remarks on semi-2-normed spaces R. Freese;S. Gahler
  8. J. Korean Math. Soc. v.29 Strictly 2-convex linear 2-normed spaces R. Freese;Y. J. Cho;S. S. Kim
  9. Math. Nachr. v.28 Lineare 2-normierte Raume S. Gahler
  10. J. Approx. Theory v.39 Best approximation in certain classes of normed linear spaces G. Godini
  11. Glasnik Mat. v.27 Linear operators on linear 2-normed spaces S. S. Kim;Y. J. Cho;A. White
  12. Math. Japon v.46 2-Pre-hilbertian 2-norms and Gateaux derivatives S. S. Kim;Y. J. Cho;A. White
  13. Doctoral Diss., Madras Univ. Orthogonality, Approximation and Fixed Points in Linear 2-Normed Spaces S. A. Mariadoss
  14. Math. Nachr. v.78 Best approximation on convex sets in metric linear spaces T. D. Narang
  15. Arch. Math. v.17 Best approximation and strict convexity of metric spaces T. D. Narang
  16. J. Approx. Theory v.22 Approximation and strong approximation in normed spaces via tangent functions P. L .Papini
  17. J. Math. Anal. and Appl. v.91 Inner product and norm derivatives P. L. Papini
  18. Mh. Math. v.88 Best coapproximation in normal linear spaces P. L. Papini;I. Singer
  19. Doctoral Diss., Madras Univ. Approximation in Linear 2-Normed Spaces and Normed Linear Spaces R. Ravi
  20. Best approximation in normal linear spaces by elements of linear subspaces I. Singer