Geodesic
On successive approximations for nonexpansive mappings in Banach spaces†
Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 6-9

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a Banach space and K a convex subset of X. A mapping Tof K into K is called a nonexpansive mapping if | T(x) – T(y) | ≦ | x – y | for all x, yεK. 
Kirk, W. A. On successive approximations for nonexpansive mappings in Banach spaces†. Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 6-9. doi: 10.1017/S0017089500001063
@article{10_1017_S0017089500001063,
     author = {Kirk, W. A.},
     title = {On successive approximations for nonexpansive mappings in {Banach} spaces{\textdagger}},
     journal = {Glasgow mathematical journal},
     pages = {6--9},
     year = {1971},
     volume = {12},
     number = {1},
     doi = {10.1017/S0017089500001063},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001063/}
}
TY  - JOUR
AU  - Kirk, W. A.
TI  - On successive approximations for nonexpansive mappings in Banach spaces†
JO  - Glasgow mathematical journal
PY  - 1971
SP  - 6
EP  - 9
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001063/
DO  - 10.1017/S0017089500001063
ID  - 10_1017_S0017089500001063
ER  - 
%0 Journal Article
%A Kirk, W. A.
%T On successive approximations for nonexpansive mappings in Banach spaces†
%J Glasgow mathematical journal
%D 1971
%P 6-9
%V 12
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001063/
%R 10.1017/S0017089500001063
%F 10_1017_S0017089500001063

[1] 1.Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U. S. A. 54 (1965), 1041–1044. Google Scholar | DOI

[2] l2.Browder, F. E., Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660–665. Google Scholar | DOI

[3] 3.Browder, F. E. and Petryshyn, W. V., The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571–575. Google Scholar | DOI

[4] 4.Edelstein, M., A remark on a theorem of M. A. Krasnoselskii, Amer. Math. Monthly 73 (1966), 509–510. Google Scholar | DOI

[5] 5.Gohde, D., Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251–258. Google Scholar | DOI

[6] 6.Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006. Google Scholar | DOI

[7] 7.Krasnoselskii, M. A., Two remarks about the method of successive approximations, Uspehi Mat. Nauk 10 (1955), no. 1 (63), 123–127. Google Scholar

[8] 8.Schaefer, H., Ober die Methode suksessiver Approximation, Jber. Deutsch. Math. Verein. 59 (1957), 131–140. Google Scholar

Cité par Sources :