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Author(s): T.D. Narang

Email(s): tdnarang1948@yahoo.co.in

Address: Department of Mathematics, Guru Nanak Dev University, Amntsar-143005 (India).

Published In:   Volume - 20,      Issue - 1,     Year - 2007


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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