On a generalization of a Greguš fixed point theorem

Ljubomir B. Ćirić

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 3, page 449-458
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Ćirić, Ljubomir B.. "On a generalization of a Greguš fixed point theorem." Czechoslovak Mathematical Journal 50.3 (2000): 449-458. <http://eudml.org/doc/30575>.

@article{Ćirić2000,
abstract = {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.},
author = {Ćirić, Ljubomir B.},
journal = {Czechoslovak Mathematical Journal},
keywords = {convex metric space; nonexpansive type mapping; fixed point; convex metric space; nonexpansive type mapping; fixed point},
language = {eng},
number = {3},
pages = {449-458},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a generalization of a Greguš fixed point theorem},
url = {http://eudml.org/doc/30575},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Ćirić, Ljubomir B.
TI - On a generalization of a Greguš fixed point theorem
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 449
EP - 458
AB - 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.
LA - eng
KW - convex metric space; nonexpansive type mapping; fixed point; convex metric space; nonexpansive type mapping; fixed point
UR - http://eudml.org/doc/30575
ER -

References

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  1. On some discontinuous fixed point mappings in convex metric spaces, Czechoslovak Math. J. 43(118) (1993), 319–326. (1993) MR1211753
  2. 10.2307/2040075, Proc. Amer. Math. Soc. 45 (1974), 267–273. (1974) DOI10.2307/2040075
  3. On a common fixed point theorem of a Greguš type, Publ. Inst. Math (Beograd) (49)63 (1991), 174–178. (1991) MR1127395
  4. A common fixed point theorem of Greguš type, Publ. Math. Debrecen 34 (1987), 83–89. (1987) MR0901008
  5. Common fixed points on a Banach space, Chung Yuan J. 11 (1982), 19–26. (1982) 
  6. 10.1155/S0161171286000030, Internat. J. Math. Math. Sci. 9 (1986), no. 1, 23–28. (1986) MR0837098DOI10.1155/S0161171286000030
  7. A fixed point theorem in Banach space, Boll. Un. Mat. Ital. A 5 (1980), 193–198. (1980) MR0562137
  8. 10.1007/BF02014826, Appl. Math. Mech. (English Ed.) 10 (1989), 183–188. (1989) DOI10.1007/BF02014826
  9. A note on a fixed point theorem of Greguš, Math. Japon. 33 (1988), 745–749. (1988) MR0972387
  10. 10.2996/kmj/1138846111, Kodai Math. Sem. Rep. 22 (1970), 142–149. (1970) Zbl0268.54048MR0267565DOI10.2996/kmj/1138846111

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