Noncommuting maps and invariant approximations

Hussain, N.; Latif, A.; Al-Mezel, S.

Artykuł - szczegóły

Tytuł artykułu

Noncommuting maps and invariant approximations

Autorzy

Hussain N. , Latif A. , Al-Mezel S.

Wybrane pełne teksty z tego czasopisma

http://www.degruyter.com/view/j/dema

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Warianty tytułu

Języki publikacji

Abstrakty

We obtain common fixed point results for generalized I-nonexpansive compatible as well as weakly compatible maps. As applications, various best approximation results for this class of maps are derived in the setup of certain metrizable topological vector spaces.

Słowa kluczowe

common fixed point compatible maps invariant approximation

punkt stały odwzorowania zgodne aproksymacja niezmienna

Wydawca

De Gruyter

Czasopismo

Demonstratio Mathematica

Rocznik

2007

Tom

Vol. 40, nr 4

Strony

895--905

Opis fizyczny

Bibliogr. 26 poz.

Twórcy

autor

Hussain N.

autor

Latif A.

autor

Al-Mezel S.

Department of Mathematics, King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Bibliografia

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[2] W. J. Dotson Jr., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Araer. Math. Soc. 38 (1973), 155-156.
[3] M. Grinc and L. Snoha, Jungck theorem for triangular maps and related results, Appl. General Topology 1 (2000), 83-92.
[4] L. Habiniak, Fizedpoint theorems and invariant approximation, J. Approx. Theory, 56 (1989), 241-244.
[5] N. Hussain and V. Berinde, Common fiied point and invariant approximation results in certain metrizable topological vector spaces, Fixed Point Theory and Appl. 2005 (2005), 1-13.
[6] N. Hussain and G. Jungck, Common fixed point and invariant approximation results for noncommuting generalized (f,g)-nonexpansive maps, J. Math. Anal. Appl. 321 (2006), 851-861.
[7] N. Hussain and A. R. Khan, Common fixed point results in best approximation theory, Appl. Math. Lett. 16 (2003), 575-580.
[8] N. Hussain, D. O'Regan and R. P. Agarwal, Common fixed point and invariant approximation results on non-starshaped domains, Georgian Math. J. 12 (2005), 659-669.
[9] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.
[10] G. Jungck, Common fized point theorems for compatible setf maps of Hausdorff topological spaces, Fixed Point Theory and Appl. 2005 (2005), 355-363.
[11] G. Jungck and N. Hussain, Compatible maps and invctriant approximations, J. Math. Anal. Appl. 325 (2007), 1003-1012.
[12] G. Jungck and S. Sessa, Fixed point theorems in best approximation theory, Math. Japon. 42 (1995), 249-252.
[13] A. R. Khan, A. Latif, A. Bano and N. Hussain, Some results on common fixed points and best approximation, Tamkang J. Math. 36 (2005), 33-38.
[14] L. A. Khan and A. R. Khan, An extention of Brosowski-Meinardus theorem on invariant approximations, Approx. Theory and Appl. 11 (1995), 1-5.
[15] G. Kothe, Topological Vector Spaces I, Springer-Verlag, Berlin, 1969.
[16] A. Latif, A result on best approximation in p-normed spaces, Arch. Math. (Brno), 37 (2001), 71-75.
[17] G. Meinardus, Invarianze bei linearen approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303.
[18] T. Okoń, Fixed point theory for Roberts spaces, Nonlinear Anal. 47 (2001), 5697-5702.
[19] D. O'Regan and N. Hussain, Generalized I-contractions and pointwise R-subweakly commuting maps, Acta Math. Sinica, 23 (8) (2007), 1505-1508.
[20] J. W. Roberts, Pathological compact convex sets in the spaces Lp, O < p < 1, University of Illinois, 1976.
[21] S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx. Theory, 55 (1988), 349-351.
[22] B. N. Sahney, K. L. Singh and J. H. M. Whitfield, Best approximation in locally convex spaces, J. Approx. Theory, 38 (1983), 182-187.
[23] N. Shahzad, Invariant approximations and R-subweakly commuting maps, J. Math. Anal. Appl. 257 (2001), 39-45.
[24] N. Shahzad, Invariant approximations, generalized I-contractions, and R-subweakly commuting maps, Fixed Point Theory and Appl. 2005 (2005), 79-86.
[25] S. P. Singh, An application of fixed point theorem to approximation theory, J. Approx. Theory, 25 (1979), 89-90.
[26] S. P. Singh, Some results on best approximation theory in locally convex spaces, J. Approx. Theory, 28 (1980), 329-333.

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Bibliografia

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bwmeta1.element.baztech-article-PWA5-0022-0016