We study best approximation in $p$-normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.
@article{107788, author = {Abdul Latif}, title = {A result on best approximation in $p$-normed spaces}, journal = {Archivum Mathematicum}, volume = {037}, year = {2001}, pages = {71-75}, zbl = {1068.41055}, mrnumber = {1822766}, language = {en}, url = {http://dml.mathdoc.fr/item/107788} }
Latif, Abdul. A result on best approximation in $p$-normed spaces. Archivum Mathematicum, Tome 037 (2001) pp. 71-75. http://gdmltest.u-ga.fr/item/107788/
Fixpunktsatze in der approximations theorie, Mathematica (Cluj) 11 (1969), 195–220. (1969) | MR 0277979
Applications of fixed point theorems, Jnanabha 19 (1989), 149–155. (1989) | MR 1060662 | Zbl 0718.41042
Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. (2) 4 (1972), 408–410. (1972) | MR 0296778
A note on fixed point theorems, J. Approx. Theory 34 (1982), 221–225. (1982) | MR 0654288 | Zbl 0483.47039
Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261–263. (1976) | MR 0400196 | Zbl 0321.54025
Fixed point theorems in best approximation theory, Math. Japon. 42 (1995), 249–252. (1995) | MR 1356383 | Zbl 0834.54026
Fixed point theory for nonexpansive mappings, Lecture Notes in Math. 886 (1981), 484–505. (1981) | MR 0643024 | Zbl 0479.47049
On best approximation in $p$-normed spaces, submitted.
Topological vector Spaces I, Springer-Verlag, Berlin, 1969. (1969) | MR 0248498 | Zbl 0179.17001
Centres asymptotiques dans certains F-espaces, Boll. Un. Mat. Ital. B(5) 17 (1980), 740–747. (1980) | MR 0580553 | Zbl 0456.47049
Invarianze bei Linearen Approximationen, Arch. Rational Mech. Anal. 14 (1963), 301–303. (1963) | MR 0156143
Weak convergence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 531–537. (1967) | MR 0211301
Functional Analysis, (second edition), McGraw-Hill, New York, 1991. (1991) | MR 1157815 | Zbl 0867.46001
An application of a fixed point theorem to approximation theory, J. Approx. Theory 25 (1979), 89–90. (1979) | MR 0526280 | Zbl 0399.41032