IJPAM: Volume 56, No. 4 (2009)

COMMON FIXED POINTS IN THE SET OF
BEST APPROXIMATIONS

N. Hussain$^1$, Marwan A. Kutbi$^2$
$^{1,2}$Department of Mathematics
King Abdul Aziz University
P.O. Box 80203, Jeddah, 21589, KINGDOM OF SAUDI ARABIA
$^1$e-mail: nhusain@kau.edu.sa
$^2$e-mail: mkutbi@Yahoo.com


Abstract.We prove a common fixed point result for noncommuting $(f,g)$-nonexpansive map $T$ and then derive certain results on best approximation. Our results generalize the results of Al-Thagafi [#!th!#], Hussain et al [#!hoa!#], Jungck and Sessa [#!js!#], Khan, Hussain and Thaheem [#!kht!#], Latif [#!la!#], [#!la1!#], Sahab et al [#!sks!#] and Singh [#!si!#].

Received: August 24, 2007

AMS Subject Classification: 46B99

Key Words and Phrases: $p$-normed space, best C-approximant, Banach operator pair, commuting maps, common fixed point, property $(N)$

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 4