Strongly unique best simulations approximation in linear 2-normed spaces

R. Vijayaragavan

doi:10.26637/mjm104/018

Abstract

In this paper we established some basic properties of the set of strongly unique best simultaneous approximation in the context of linear 2-normed space.

Keywords:

Linear 2-normed space, strongly unique best approximation, best simultaneous approximation and strongly unique best simultaneous approximation

Mathematics Subject Classification:

41A50, 41A52, 41A99, 41A28

Authors Imprint References Funding Related Articles Downloads

R. Vijayaragavan School of Advanced Sciences, V I T University, Vellore-632014, Tamil Nadu, India.

Pages: 157-162
Date Published: 01-10-2013
Vol. 1 No. 04 (2013): Malaya Journal of Matematik (MJM)

Y.J. Cho, Theory of 2-inner Product Spaces, Nova Science Publications, New York, 1994.

J.B. Diaz and H.W.McLaughlin, On simultaneous Chebyshev approximation of a set of bounded complex-valued functions, J. Approx Theory, 2(1969), 419-432. DOI: https://doi.org/10.1016/0021-9045(69)90011-2

J.B. Diaz and H.W.McLaughlin, On simultaneous Chebyshev approximation and Chebyshev approximation with an additive weight function, J. Approx Theory, 6(1972), 68-71. DOI: https://doi.org/10.1016/0021-9045(72)90082-2

C.B. Dunham, Simultaneous Chebyshev approximation of functions on an interval, Proc. Amer. Math. Soc., 18(1967), 472-477. DOI: https://doi.org/10.1090/S0002-9939-1967-0212463-6

D.S. Goel, A.S.B. Holland, C. Nasim and B.N.Sahney, On best simultaneous approximation in normed linear spaces. Canad. Math. Bull., 17(4)(1974), 523-527. DOI: https://doi.org/10.4153/CMB-1974-092-5

D.S. Goel, A.S.B. Holland, C. Nasim, and B.N.Sahney, Characterization of an element of best L p −simultaneous approximation, S.R.Ramanujan Memorial Volume, Madras, 1974, 10-14.

P.J. Laurent and D.V. Pai, Simultaneous approximation of vector valued functions, Research Report, MRR03-97, Department of Mathematics, IIT, Bombay, 1997.

W.H. Ling, H.W. McLaughlin and M.L. Smith, Approximation of random functions, AMS Notices, 22(1975), A-161.

D.V. Pai, Characterization of strong uniqueness of best simultaneous approximation, in Proceedings of the Fifth Annual Conference of Indian Society of Industrial and Applied Mathematics (ISIAM), Bhopal, 1998.

D.V. Pai and K. Indira, Strong unicity in simultaneous approximation, in Proceedings of the Conference on Analysis, Wavelets and Applications, Feb. 12-14, 2000.

G.H. Phillips and B.N. Sahney, Best simultaneous approximation in the L 1 and L 2 norms, in Proceeding of conference on theory of Approximation at University of Calgary (August 1975), Academic Press, New York.