Proximinality and co-proximinality in metric linear spaces

T. W. Narang, Sahil Gupta

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.

Keywords


Best approximation; best coapproximation; proximinal set; co-proximinal set; Chebyshev set; co-Chebyshev set

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References


Cheney, E. W., Introduction to Approximation Theory, McGraw Hill, New York, 1966.

Franchetti, C., Furi, M., Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 1045–1048.

Mazaheri, H., Maalek Ghaini, F. M., Quasi-orthogonality of the best approximant sets, Nonlinear Anal. 65 (2006), 534–537.

Mazaheri, H., Modaress, S. M. S., Some results concerning proximinality and coproximinality, Nonlinear Anal. 62 (2005), 1123–1126.

Muthukumar, S., A note on best and best simultaneous approximation, Indian J. Pure Appl. Math. 11 (1980), 715–719.

Narang, T. D., Best approximation in metric spaces, Publ. Sec. Mat. Univ. Autonoma Barcelona 27 (1983), 71–80.




DOI: http://dx.doi.org/10.17951/a.2015.69.1.83
Date of publication: 2015-11-30 09:21:12
Date of submission: 2015-09-03 12:39:27


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