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Abstrakty
A general common fixed point result is obtained for commuting maps on non-starshaped domain in a p-normed space. As applications, we obtain Brosowski-Meinardus type approximation theorems in p-normed spaces which are not necessarily locally convex. Recent approximation results of a number of authors follow as a consequence of our results.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
675--681
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
autor
- Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Bibliografia
- [1] M. A. Al-Thagafi, Common fixed points and, best approximation, J. Approx. Theory 85(3) (1996), 318-323.
- [2] B. Brosowski, Fix Punktsatze in der approximations theorie, Mathematica (Cluj) 11 (1969), 195-220.
- [3] W. J. Dotson Jr., Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. 4 (1972), 408-410.
- [4] W. J. Dotson Jr., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155-156.
- [5] T. L. Hicks, M.D. Humphries, A note on fixed point theorems, J. Approx. Theory 34 (1982), 221-225.
- [6] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.
- [7] G. Jungck, S. Sessa, Fixed point theorems in best approximation theory, Math. Japon. 42(2) (1995), 249-252.
- [8] A. R. Khan, N. Hussain, A. B. Thaheem, Applications of fixed point theorems to invariant approximation, Approx. Theory and Appl. 16 (2000), 48-55.
- [9] L. A. Khan, A. R. Khan, An extention of Brosowski-Meinardus theorem on invariant approximations, Approx. Theory and Appl. 11 (1995), 1-5.
- [10] L. A. Khan and A. Latif, Some results on common fixed points and best approximation in p-normed spaces, Demonstratio Math. 34 (2001), 831-836.
- [11] G. Köthe, Topological Vector Spaces. 1, Springer-Verlag New York Inc., New York, 1969.
- [12] A. Latif, A result on best approximation in p-normed spaces, Arch. Math. 37 (2001), 71-75.
- [13] G. Meinardus, Invarianze bei linearen approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303.
- [14] S. A. Sahab, M. S. Khan, S. Sessa, A result in best approximation theory, J. Approx. Theory 55 (1988), 349-351.
- [15] S. P. Singh, An application of fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89-90.
- [16] P. V. Subrahmanyam, An application of a fixed point theorem to best approximation, J. Approx. Theory 20 (1977), 165-172.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA3-0007-0020