Geodesic
On a generalization of a Greguš fixed point theorem
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 449-458 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $C$ be a closed convex subset of a complete convex metric space $X$. In this paper a class of selfmappings on $C$, which satisfy the nonexpansive type condition $(2)$ below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
Let $C$ be a closed convex subset of a complete convex metric space $X$. In this paper a class of selfmappings on $C$, which satisfy the nonexpansive type condition $(2)$ below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
Classification : 47H10, 54H25
Keywords: convex metric space; nonexpansive type mapping; fixed point 
@article{CMJ_2000_50_3_a0,
     author = {\'Ciri\'c, Ljubomir},
     title = {On a generalization of a {Gregu\v{s}} fixed point theorem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {449--458},
     year = {2000},
     volume = {50},
     number = {3},
     mrnumber = {1777468},
     zbl = {1079.47509},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a0/}
}
TY  - JOUR
AU  - Ćirić, Ljubomir
TI  - On a generalization of a Greguš fixed point theorem
JO  - Czechoslovak Mathematical Journal
PY  - 2000
SP  - 449
EP  - 458
VL  - 50
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a0/
LA  - en
ID  - CMJ_2000_50_3_a0
ER  - 
%0 Journal Article
%A Ćirić, Ljubomir
%T On a generalization of a Greguš fixed point theorem
%J Czechoslovak Mathematical Journal
%D 2000
%P 449-458
%V 50
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a0/
%G en
%F CMJ_2000_50_3_a0
Ćirić, Ljubomir. On a generalization of a Greguš fixed point theorem. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 3, pp. 449-458. http://geodesic.mathdoc.fr/item/CMJ_2000_50_3_a0/

[LJC93] LJ. B. Ćirić: On some discontinuous fixed point mappings in convex metric spaces. Czechoslovak Math. J. 43(118) (1993), 319–326. | MR

[LJC74] LJ. B. Ćirić: A generalization of Banach’s contraction principle. Proc. Amer. Math. Soc. 45 (1974), 267–273. | DOI

[LJC91] LJ. B. Ćirić: On a common fixed point theorem of a Greguš type. Publ. Inst. Math (Beograd) (49)63 (1991), 174–178. | MR

[MD87] M. L. Diviccaro, B. Fisher, S. Sessa: A common fixed point theorem of Greguš type. Publ. Math. Debrecen 34 (1987), 83–89. | MR

[BF82] B. Fisher: Common fixed points on a Banach space. Chung Yuan J. 11 (1982), 19–26.

[BF86] B. Fisher, S. Sessa: On a fixed point theorem of Greguš. Internat. J. Math. Math. Sci. 9 (1986), no. 1, 23–28. | DOI | MR

[MG80] M. Greguš: A fixed point theorem in Banach space. Boll. Un. Mat. Ital. A 5 (1980), 193–198. | MR

[BL89] B. Y. Li: Fixed point theorems of nonexpansive mappings in convex metric spaces. Appl. Math. Mech. (English Ed.) 10 (1989), 183–188. | DOI

[RM88] R. N. Mukherjea, V. Verma: A note on a fixed point theorem of Greguš. Math. Japon. 33 (1988), 745–749. | MR

[WT70] W. Takahashi: A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22 (1970), 142–149. | DOI | MR | Zbl