| Title:
|
On a generalization of a Greguš fixed point theorem (English) |
| Author:
|
Ćirić, Ljubomir |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
449-458 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
convex metric space |
| Keyword:
|
nonexpansive type mapping |
| Keyword:
|
fixed point |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1079.47509 |
| idMR:
|
MR1777468 |
| . |
| Date available:
|
2009-09-24T10:34:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127584 |
| . |
| Reference:
|
[LJC93] LJ. B. Ćirić: On some discontinuous fixed point mappings in convex metric spaces.Czechoslovak Math. J. 43(118) (1993), 319–326. MR 1211753 |
| Reference:
|
[LJC74] LJ. B. Ćirić: A generalization of Banach’s contraction principle.Proc. Amer. Math. Soc. 45 (1974), 267–273. 10.2307/2040075 |
| Reference:
|
[LJC91] LJ. B. Ćirić: On a common fixed point theorem of a Greguš type.Publ. Inst. Math (Beograd) (49)63 (1991), 174–178. MR 1127395 |
| Reference:
|
[MD87] M. L. Diviccaro, B. Fisher, S. Sessa: A common fixed point theorem of Greguš type.Publ. Math. Debrecen 34 (1987), 83–89. MR 0901008 |
| Reference:
|
[BF82] B. Fisher: Common fixed points on a Banach space.Chung Yuan J. 11 (1982), 19–26. |
| Reference:
|
[BF86] B. Fisher, S. Sessa: On a fixed point theorem of Greguš.Internat. J. Math. Math. Sci. 9 (1986), no. 1, 23–28. MR 0837098, 10.1155/S0161171286000030 |
| Reference:
|
[MG80] M. Greguš: A fixed point theorem in Banach space.Boll. Un. Mat. Ital. A 5 (1980), 193–198. MR 0562137 |
| Reference:
|
[BL89] B. Y. Li: Fixed point theorems of nonexpansive mappings in convex metric spaces.Appl. Math. Mech. (English Ed.) 10 (1989), 183–188. 10.1007/BF02014826 |
| Reference:
|
[RM88] R. N. Mukherjea, V. Verma: A note on a fixed point theorem of Greguš.Math. Japon. 33 (1988), 745–749. MR 0972387 |
| Reference:
|
[WT70] W. Takahashi: A convexity in metric space and nonexpansive mappings I.Kodai Math. Sem. Rep. 22 (1970), 142–149. Zbl 0268.54048, MR 0267565, 10.2996/kmj/1138846111 |
| . |
