Some results on common fixed points and best approximation in p-normed spaces

• Autorzy: Khan L. , Latif A.
• Języki publikacji: EN

Abstrakty

EN

A general common fixed point result is obtained for commuting maps in p-normed spaces. The Brosowski-Meinardus type approximation theorem in p-normed spaces via our main result is derived. These results unify and include the recent work of Jungck and Sessa [6], Khan and Khan [7], Sahab, Khan and Sessa [II], Singh [12] etc.

Słowa kluczowe

EN

best C-approximants; common fixed points; commuting map; locally G-contractive map

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 831--836
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Khan L.

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

autor

Latif A.

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

Bibliografia

• [1] B. Brosowski, Fixpunktsatze in der approximations theorie, Mathematica (Cluj) 11 (1969), 195-220.
• [2] W. G. Dotson, Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. (2) 4 (1972), 408-410.
• [3] L. Habiniak, Fixed point theorems and invariant approximation, J. Approx. Theory 56 (1989), 241-244.
• [4] T. L. Hicks and M. D. Humphries, A note on fixed point theorems, J. Approx. Theory 34 (1982), 221-225.
• [5] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.
• [6] G. Jungck and S. Sessa, Fixed point theorems in best approximation theory, Math. Japonica 42 (1995), 249-252.
• [7] L. A. Khan and A. R. Khan, An extension of Brosowki-Meinardus theorem on invariant approximation, Approx. Theory & its Appl. 11 (1995), 1-5.
• [8] G. Kothe, Topological Vector Spaces I, Springer, Berlin, 1969.
• [9] A. Latif, A result on best approximation in p-normed spaces, Arch. Math. (Brno) 37 (2001), 71-75.
• [10] G. Meinardus, Invarianze bei Linearen Approximationen, Arch. Rational Mech. Anal. 14 (1963), 301-303.
• [11] S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx. Theory 55 (1988), 349-351.
• [12] S. P. Singh, An application of a fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89-90.