SOME COMMON FIXED POINT RESULTS IN NON-NORMAL CONE METRIC SPACES

Volume 3, Issue 3, pp 193-202 http://dx.doi.org/10.22436/jnsa.003.03.06

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1491 Downloads
• 2425 Views

Authors

ZORAN KADELBURG - Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Beograd, Serbia. STOJAN RADENOVIĆ - Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.

Abstract

The aim of this paper is to obtain extended variants of some common fixed point results in cone metric spaces in the case that the underlying cone is not normal. The first result concerns g-quasicontractions of D. Ilić and V. Rakočević [Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876-882], and the second is concerned with Hardy-Rogers-type conditions and extends some recent results of M. Abbas, B. E. Rhoades and T. Nazir [Common fixed points for four maps in cone metric spaces, Appl. Math. Comput. 216 (2010), 80-86].

Share and Cite

Keywords

• Common fixed point
• ordered Banach space
• cone metric space
• normal and non-normal cone
• weakly compatible mappings.

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, G. Jungck, Common Fixed point results of noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 418-420.


• [2] M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22 (2009), 511-515.


• [3] M. Abbas, B. E. Rhoades, T. Nazir, Common fixed points for four maps in cone metric spaces, Appl. Math. Comput., 216 (2010), 80-86.


• [4] Lj. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.


• [5] K. M. Das, K. V. Naik, Common fixed point theorems for commuting maps on cone metric spaces, Proc. Amer. Math. Soc., 77 (1979), 369-373.


• [6] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, (1985)


• [7] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1467-1475.


• [8] D. Ilić, V. Rakočević, Common fixed points for maps on cone metric space , J. Math. Anal. Appl., 341 (2008), 876-882.


• [9] D. Ilić, V. Rakočević, Quasi-contraction on cone metric space, Appl. Math. Lett. , 22 (2009), 728-731.


• [10] G. Jungck , Common fixed points for noncontinuous nonself maps on nonmetric spacers, Far East J. Math. Sci., 4 (1986), 199-215.


• [11] G. Jungck, S. Radenović, S. Radojević, V. Rakočević, Common fixed point theorems for qeakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., Article ID 643840, doi:10.1155/2009/643840. , 2009 (2009), 13 pages


• [12] Z. Kadelburg, M. Pavlović, S. Radenović, Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl., 59 (2010), 3148-3159.


• [13] Z. Kadelburg, S. Radenović, V. Rakočević, Remarks on ''Quasi-contraction on a cone metric space'', Appl. Math. Lett. , 22 (2009), 1674-1679.


• [14] Z. Kadelburg, S. Radenović, V. Rakočević, Topological vector space valued cone metric spaces and fixed point theorems, Fixed Point Theory Appl., (in press. ),


• [15] Sh. Rezapour, R. H. Haghi, N. Shahzad, Some notes on fixed points of quasi-contraction maps, Appl. Math. Lett., 23 (2010), 498-502.