Proximinality and co-proximinality in metric linear spaces

T.D. Narang; Sahil Gupta

Annales UMCS, Mathematica (2015)

  • Volume: 69, Issue: 1, page 83-90
  • ISSN: 2083-7402

Abstract

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As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces

How to cite

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T.D. Narang, and Sahil Gupta. "Proximinality and co-proximinality in metric linear spaces." Annales UMCS, Mathematica 69.1 (2015): 83-90. <http://eudml.org/doc/270799>.

@article{T2015,
abstract = {As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces},
author = {T.D. Narang, Sahil Gupta},
journal = {Annales UMCS, Mathematica},
keywords = {Best approximation; best coapproximation; proximinal set; co-proximinal set; Chebyshev set; co-Chebyshev set.; best approximation; co-Chebyshev set},
language = {eng},
number = {1},
pages = {83-90},
title = {Proximinality and co-proximinality in metric linear spaces},
url = {http://eudml.org/doc/270799},
volume = {69},
year = {2015},
}

TY - JOUR
AU - T.D. Narang
AU - Sahil Gupta
TI - Proximinality and co-proximinality in metric linear spaces
JO - Annales UMCS, Mathematica
PY - 2015
VL - 69
IS - 1
SP - 83
EP - 90
AB - As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces
LA - eng
KW - Best approximation; best coapproximation; proximinal set; co-proximinal set; Chebyshev set; co-Chebyshev set.; best approximation; co-Chebyshev set
UR - http://eudml.org/doc/270799
ER -

References

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  1. [1] Cheney, E. W., Introduction to Approximation Theory, McGraw Hill, New York, 1966. Zbl0161.25202
  2. [2] Franchetti, C., Furi, M., Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 1045-1048. Zbl0245.46024
  3. [3] Mazaheri, H., Maalek Ghaini, F. M., Quasi-orthogonality of the best approximant sets, Nonlinear Anal. 65 (2006), 534-537. Zbl1106.41033
  4. [4] Mazaheri, H., Modaress, S. M. S., Some results concerning proximinality and coproximinality, Nonlinear Anal. 62 (2005), 1123-1126. Zbl1075.41017
  5. [5] Muthukumar, S., A note on best and best simultaneous approximation, Indian J. Pure Appl. Math. 11 (1980), 715-719. Zbl0433.41011
  6. [6] Narang, T. D., Best approximation in metric spaces, Publ. Sec. Mat. Univ. Autonoma Barcelona 27 (1983), 71-80. Zbl0596.41050
  7. [7] Narang, T. D., Best approximation in metric linear spaces, Math. Today 5 (1987), 21-28. Zbl0624.41038
  8. [8] Narang, T. D., Singh, S. P., Best coapproximation in metric linear spaces, Tamkang J. Math. 30 (1999), 241-252. Zbl0987.41012
  9. [9] Papini, P. L., Singer, I., Best coapproximation in normed linear spaces, Monatsh. Math. 88 (1979), 27-44. Zbl0421.41017
  10. [10] Rao, K. Chandrasekhara, Functional Analysis, Narosa Publishing House, New Delhi, 2002. Zbl1235.11009
  11. [11] Singer, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York, 1970. Zbl0197.38601

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