Self-similar sets and fractals generated by Ćirić type operators
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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
ISRP Style
Adrian Petruşel, Anna Soos, Self-similar sets and fractals generated by Ćirić type operators, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 1048--1058
AMA Style
Petruşel Adrian, Soos Anna, Self-similar sets and fractals generated by Ćirić type operators. J. Nonlinear Sci. Appl. (2015); 8(6):1048--1058
Chicago/Turabian Style
Petruşel, Adrian, Soos, Anna. "Self-similar sets and fractals generated by Ćirić type operators." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 1048--1058
Keywords
- Fixed point
- strict fixed point
- metric space
- self-similar set
- fractal
- generalized contraction.
MSC
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)