ε-simultaneous approximation and invariant points

In this paper we generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of epsilon-simultaneous approximation. As a consequence some results on epsilon-approximation and best approximation are also deduced. The results proved extend and generalize some of the results of R.N. Mukherjee and V. Verma [Bull. Cal. Math. Soc. 81(1989) 191-196; Publ. de l'Inst. Math. 49(1991) 111-116], T.D. Narang and S. Chandok [Mat. Vesnik 61(2009) 165-171; Selcuk J. Appl. Math. 10(2009) 75-80; Indian J. Math. 51(2009) 293-303], G.S. Rao and S.A. Mariadoss [Serdica-Bulgaricae Math. Publ. 9(1983) 244-248] and of few others.