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Invariant points of best approximation and best simultaneous approximation

Chandok S., Narang T.D.

Fasciculi Mathematici

2013

Nr 51

61-70

In this paper we generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(1991) 111-116], T.D. Narang and S. Chandok [Selcuk J. Appl. Math. 10(2009) 75-80; Indian J. Math. 51(2009) 293-303], and of G. S. Rao and S. A. Mariadoss [Serdica-Bulgaricae Math. Publ. 9(1983) 244-248].