Cite this article:
Narang (2013). On Generalisations of Ky Fan's Theorem in Metric Linear Spaces. Journal of Ravishankar University (Part-B: Science), 26(1), pp. 35-39.
Journal of Ravishankar-B 26(1), 35-39 (2013)
On Generalisations of Ky Fan's Theorem in Metric Linear Spaces
T.D.
Narang
Department
of Mathematics, Guru Nanak Dev University, Amritsar-143005 (India)
Abstract: In 1969, Ky Fan
[Math. Z. 112(1969), 234-240] proved that if M
is a nonempty compact convex subset of a normed linear space Ethen for any continuous map f: M→ E, there exists a y0€ M such that 11 y0 - f(y0) 11 = Min { 11 x -
f(y0) l I: x€M}
This theorem has
been extended by several mathematicians and applied in various fields.
This
paper
also deals with some further generalizations of the result in metric linear spaces.
Keywords: Best
approximation, approximatively compact set, convex set, almost affine map, almost
quasi convex map
Corresponding Author: tdnarang1948@yahoo.co.in
NOTE: Full version of this manuscript is available in PDF.