ĆIRIĆ'S FIXED POINT THEOREM IN A CONE METRIC SPACE

Volume 3, Issue 4, pp 302-308 http://dx.doi.org/10.22436/jnsa.003.04.09

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)

• 1690 Downloads
• 2705 Views

Authors

BESSEM SAMET - Département de Mathématiques, École Supérieure des Sciences et Techniques de Tunis, 5, Avenue Taha Hussein-Tunis, B. P. 56, Bab Menara-1008, Tunisie.

Abstract

In this paper, we extend a fixed point theorem due to Ćirić to a cone metric space.

Share and Cite

Keywords

• Ćirić's theorem
• Cone metric space
• Fixed point.

MSC

•  54H25
•  47H10

References

• [1] M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. , 341 (2008), 416-420.


• [2] A. Azam, M. Arshad, I. Beg, Common fixed points of two maps in cone metric spaces , Rend. Circ. Mat. Palermo. , 57 (2008), 433-441.


• [3] A. Azam, M. Arshad, I. Beg, Common fixed point theorems in cone metric spaces, J. Nonlinear Sci. Appl. , 2 (4) (2009), 204-213.


• [4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. , 3 (1922), 133-181.


• [5] I. Beg, M. Abbas, T. Nazir, Generalized cone metric spaces, J. Nonlinear Sci. Appl. , 3 (1) (2010), 21-31.


• [6] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. , 65 (2006), 1379-1393.


• [7] D. W. Boyd, J. S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. , 20 (1969), 458-464.


• [8] L. B. Ćirić, Generalized contractions and fixed point theorems, Publ. L'Inst. Math. , 12 (26) (1971), 19-26.


• [9] L. B. Ćirić, Fixed points for generalized multi-valued mappings, Mat. Vesnik , 9 (24) (1972), 265-272.


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


• [11] L. B. Ćirić, Non-self mappings satisfying nonlinear contractive condition with applications, Nonlinear Anal. , 71 (2009), 2927-2935.


• [12] L-G. Huang, X. Zhang , Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. , 332 (2007), 1468-1476.


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


• [14] M. Jleli, B. Samet, The Kannan's fixed point theorem in a cone rectangular metric space, J. Nonlinear Sci. Appl. , 2 (3) (2009), 161-167.


• [15] V. Lakshmikantham, L. B. Ćirić , Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. , 70 (2009), 4341-4349.


• [16] S. Rezapour, R. Hamlbarani, Some notes on the paper ''Cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl. , 345 (2008), 719-724.


• [17] B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., doi:10.1016/j.na.2010.02.026. (2010)