Open Access
december 2011 ε-simultaneous approximation and invariant points
Sumit Chandok, T.D. Narang
Bull. Belg. Math. Soc. Simon Stevin 18(5): 821-834 (december 2011). DOI: 10.36045/bbms/1323787169


In this paper we generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of ε-simultaneous approximation. As a consequence some results on ε-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; Selçuk 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.


Download Citation

Sumit Chandok. T.D. Narang. "ε-simultaneous approximation and invariant points." Bull. Belg. Math. Soc. Simon Stevin 18 (5) 821 - 834, december 2011.


Published: december 2011
First available in Project Euclid: 13 December 2011

zbMATH: 1220.41003
MathSciNet: MR2918648
Digital Object Identifier: 10.36045/bbms/1323787169

Primary: 41A28 , 41A50 , 47H10 , 54H25

Keywords: Best approximation , best simultaneous approximation , jointly continuous contractive family , nonexpansive and quasi-nonexpansive mappings , starshaped set , ε-simultaneous approximation , ε-simultaneous approximatively compact set

Rights: Copyright © 2011 The Belgian Mathematical Society

Vol.18 • No. 5 • december 2011
Back to Top