Bulletin of the Belgian Mathematical Society - Simon Stevin

ε-simultaneous approximation and invariant points

Sumit Chandok and T.D. Narang

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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.

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Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 5 (2011), 821-834.

First available in Project Euclid: 13 December 2011

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Zentralblatt MATH identifier

Primary: 41A28: Simultaneous approximation 41A50: Best approximation, Chebyshev systems 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]

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


Chandok, Sumit; Narang, T.D. ε-simultaneous approximation and invariant points. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 5, 821--834. doi:10.36045/bbms/1323787169. https://projecteuclid.org/euclid.bbms/1323787169

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