Common fixed point and invariant approximation results

• Autorzy: Hussain N.
• Języki publikacji: EN

Abstrakty

EN

We extend the concept of R-subweakly commuting maps due to Shahzad [21] to the case of non-starshaped domain and obtain common fixed point results for this class of maps on non-starshaped domain in the setup of p-normed spaces. As applications, we establish Brosowski-Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa, Singh and Shahzad.

Słowa kluczowe

EN

fixed point theorem; invariant approximation; R-subweakly commuting

PL

twierdzenie o punkcie stałym; punkty stałe; aproksymacja niezmienna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 2
• Strony: 389--400
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Hussain N.

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

Bibliografia

• [1] M. A. Al -Thagafi, Common fixed points and best approximation, J. Approx. Theory 85(3) (1996), 318-323.
• [2] I. Beg, A. R. Khan and N. Hus sain, Approximation of *-nonexpansive random multivalued operators on Banach spaces, J. Aust. Math. Soc. 76 (2004), 51-66.
• [3] Brosowski, Fix Punktsatze in der approximations theorie, Mathematica (Cluj) 11 (1969), 195-220.
• [4] 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.
• [5] W. J. Dotson Jr., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155-156.
• [6] L. Habiniak, Fixed point theorems and invariant approximation, J. Approx. Theory, 56 (1989), 241-244.
• [7] T. L. Hicks and M. D. Humphries, A note on fixed point theorems, J. Approx. Theory 34 (1982), 221-225.
• [8] N. Hussain and A. R. Khan, Common fixed point results in best approximation theory, Applied Math. Lett. 16 (2003), 575-580.
• [9] N. Hussain and A. R. Khan, Common fixed points and best approximation in p-normed spaces, Demonstratio Math. 36 (2003), 675-681.
• [10] G. Jungck and S. Sessa, Fixed point theorems in best approximation theory, Math. Japon. 42(2) (1995), 249-252.
• [11] A. R. Khan, N. Hussain and A. B. Thaheem, Applications of fixed point theorems to invariant approximation, Approx. Theory and Appl. 16 (2000), 48-55.
• [12] G. Kothe, Topological Vector Spaces 1, Springer-Verlag New York Inc., New York, 1969.
• [13] A. Latif, A result on best approximation in p-normed spaces, Arch. Math. 37 (2001), 71-75.
• [14] G. Meinardus, Invarianze bei linearen approximationen, Arch. RationalMech. Anal. 14 (1963), 301-303.
• [15] S. A. Naimpally, K. L. Singh and J. H. M. Whitfield, Fixed points and nonexpansive retracts in locally convex spaces, Fund. Math. CXX (1984), 63-75.
• [16] R. P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436-44.
• [17] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973.
• [18] S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx. Theory 55 (1988), 349-351.
• [19] N. Shahzad, A result on best approximation, Tamkang J. Math. 29(3) (1989), 223-226; corrections 30 (1999), 165.
• [20] N. Shahzad, Noncommuting maps and best approximations, Rad. Math. 10 (2001), 77-83.
• [21] N. Shahzad, Invariant approximations and R-subweakly commuting maps, J Math. Anal. Appl. 257 (2001), 39-45.
• [22] S. P. Singh, An application of fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89-90.
• [23] P. V. Subrahmanyam, An application of a fixed point theorem to best approximation, J. Approx. Theory 20 (1977), 165-172.
• [24] K. K. Tan and X. Z. Yaun, Random fixed point theorems and approximation in cones, J. Math. Anal. Appl. 185 (1994), 378-390.