Proximinality and co-proximinality in metric linear spaces
T.D. Narang ; Sahil Gupta
Annales UMCS, Mathematica, Tome 68 (2015), p. 83-90 / Harvested from The Polish Digital Mathematics Library
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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

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270799 
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     volume = {68},
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     zbl = {1321.41044},
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T.D. Narang; Sahil Gupta. Proximinality and co-proximinality in metric linear spaces. Annales UMCS, Mathematica, Tome 68 (2015) pp. 83-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0014/

[1] Cheney, E. W., Introduction to Approximation Theory, McGraw Hill, New York, 1966. | Zbl 0161.25202

[2] Franchetti, C., Furi, M., Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 1045-1048. | Zbl 0245.46024

[3] Mazaheri, H., Maalek Ghaini, F. M., Quasi-orthogonality of the best approximant sets, Nonlinear Anal. 65 (2006), 534-537. | Zbl 1106.41033

[4] Mazaheri, H., Modaress, S. M. S., Some results concerning proximinality and coproximinality, Nonlinear Anal. 62 (2005), 1123-1126. | Zbl 1075.41017

[5] Muthukumar, S., A note on best and best simultaneous approximation, Indian J. Pure Appl. Math. 11 (1980), 715-719. | Zbl 0433.41011

[6] Narang, T. D., Best approximation in metric spaces, Publ. Sec. Mat. Univ. Autonoma Barcelona 27 (1983), 71-80. | Zbl 0596.41050

[7] Narang, T. D., Best approximation in metric linear spaces, Math. Today 5 (1987), 21-28. | Zbl 0624.41038

[8] Narang, T. D., Singh, S. P., Best coapproximation in metric linear spaces, Tamkang J. Math. 30 (1999), 241-252. | Zbl 0987.41012

[9] Papini, P. L., Singer, I., Best coapproximation in normed linear spaces, Monatsh. Math. 88 (1979), 27-44. | Zbl 0421.41017

[10] Rao, K. Chandrasekhara, Functional Analysis, Narosa Publishing House, New Delhi, 2002. | Zbl 1235.11009

[11] Singer, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York, 1970. | Zbl 0197.38601