Self-similar sets and fractals generated by Ćirić type operators

Volume 8, Issue 6, pp 1048--1058 http://dx.doi.org/10.22436/jnsa.008.06.15

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)

• 1393 Downloads
• 2579 Views

Authors

Adrian Petruşel - Department of Mathematics, Babeş-Bolyai University, Kogalniceanu Street no. 1, 400084 Cluj-Napoca, Romania. Anna Soos - Department of Mathematics, Babeş-Bolyai University, Kogalniceanu Street no. 1, 400084 Cluj-Napoca, Romania.

Abstract

The purpose of this paper is to present fixed point, strict fixed point and fixed set results for (singlevalued and multivalued) generalized contractions of Ćirić type. The connections between fixed point theory and the theory of self-similar sets is also discussed.

Share and Cite

Keywords

• Fixed point
• strict fixed point
• metric space
• self-similar set
• fractal
• generalized contraction.

MSC

•  47H10
•  54H25

References

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


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


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


• [4] L. B. Ćirić, Contractive type non-self mappings on metric spaces of hyperbolic type, J. Math. Anal. Appl., 317 (2006), 28-42.


• [5] G. E. Hardy, T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16 (1973), 201-206.


• [6] A. Petruşel , Ćirić type fixed point theorems, Stud. Univ. Babeş-Bolyai Math., 59 (2014), 233-245.


• [7] A. Petruşel, G. Petruşel, Multivalued Picard operator, J. Nonlinear Convex Anal., 13 (2012), 157-171.


• [8] A. Petruşel, I. A. Rus, M. A. Şerban, The multifractal operator and iterated multifunction systems generated by nonself multivalued operators, Set-Valued Var. Anal., (in press),


• [9] S. Reich, Fixed point of contractive functions, Boll. Un. Mat. Ital., 5 (1972), 26-42.


• [10] B. E. Rhoades , A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257-288.


• [11] I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, (2001)


• [12] M. Yamaguti, M. Hata, J. Kigani, Mathematics of Fractals, Translations Math. Monograph, Vol. 167, Amer. Math. Soc. Providence (1997)