Skip to main content
Log in

On a generalization of a Greguš fixed point theorem

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

  2. LJ. B. Ćirić: A generalization of Banach's contraction principle. Proc. Amer. Math. Soc. 45 (1974), 267–273.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  6. B. Fisher, S. Sessa: On a fixed point theorem of Greguš. Internat. J. Math. Math. Sci. 9 (1986), no. 1, 23–28.

    Google Scholar 

  7. M. Greguš: A fixed point theorem in Banach space. Boll. Un. Mat. Ital. A 5 (1980), 193–198.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. W. Takahashi: A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22 (1970), 142–149.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ćirić, L. On a generalization of a Greguš fixed point theorem. Czechoslovak Mathematical Journal 50, 449–458 (2000). https://doi.org/10.1023/A:1022870007274

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022870007274

Navigation