Cite this article:
Narang (2007). Best Approximation And Common Fixed Points Of Non-Commuting Mappings. Journal of Ravishankar University (Part-B: Science), 20(1), pp.25-30.
Journal of Ravishankar
University Vol. 20 No. B (Science) 2007 PP 25-30 ISSN 0970-5910
Best Approximation And Common Fixed Points Of Non-Commuting
Mappings
T.D.Narang
Department of Mathematics, Guru Nanak Dev University, Amntsar-143005 (India),
E-mail: tdnarang1948@yahoo.co.in
MS Received: 23/09/06
Accepted: 05/10/2007
Abstract-
Using a common fixed point
theorem of Naseer Shahzad
[Rad. Mat. 10 (2001), 77] for non-commuting mappings, we improve
and extend several known
results (including those of I. Beg, N. Shahzad and
M. Iqbal [Approx. Theory
and Appl. 8 (1992),
97], 8. Brosowski [Mathematica (cluj) 11(1969),195],
T.L.Hicks and M.O.Humphries
[J. Approx. Theory 34 (1982), 221], Abdul-Rahim Khan, Arjamand Sano and Nawab Hussain
[Int. J, Pure Appl. Math. 2 (2002), 411]. G.Meinardus [Arch. Rational
Mech. Anal. 14 {1963),
301], Asia
Naz [Radovi Matematicki, 10(2001), 203). Salem A. Sahab
and M.S. Khan [Review
of Research, 17(1987),
143;
Bull. Institute Math. Acad. Sinica
17 (1989),
75], Salem A. Sahab,M.S. Khan and S. Sessa [J. Approx. Theory
55 {1988), 349],
Naseer Shahzad [Tamkang J. Math. 29(1998),
223] and S.P.Singh [J. Approx. Theory
25 (1979), 89; Applied Nonlinear Analysis (Ed. V.
Lakshmikanathan), Academic Press, New York (1979), 389]) on common
fixed
points
of commuting and non-commuting mappings and bast approximation.
Keywords: Best Approximation, Convex Metric Space,
Convex Set, Starshaped Set. Affine Map,
Weakly Commuting
Map.
Using fixed point theory. Meinardus
(1963) was the first to establish the existence
of an invariant approximation. Brosowski
(1969) obtained the. following result on invariant
approximation
generalizing the result of
Meinardus{1963): This research was supported by University Grants Commission, India (F.30-238/2004(SR).
AMS Subject Classification (2000):
41A50, 41A65, 47H10,
54H25
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