Iterated function system of locally contractive operators
DOI:
https://doi.org/10.33993/jnaat332-779Keywords:
fixed point, self-similar set, locally contractive type operatorAbstract
The aim of this paper is to study the properties of the fractal and the multi-fractal operator generated by some iterated function system satisfying to a locally contractive type condition.Downloads
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Andres, J., Some standard fixed-point theorems revisited, Atti Sem. Mat. Fis. Univ. Modena, 49, pp. 455-471, 2001.
Andres, J. and Fišer, J., Metric and topological fractals, Int. J. Bifurc. Chaos, 14, 2004, pp. 1277-1289, https://doi.org/10.1142/s021812740400979x DOI: https://doi.org/10.1142/S021812740400979X
Andres, J. and Fišer, J., Fractals generated by diffential equations, Dynam. Systems Appl., 11, pp. 471-479, 2002.
Andres J. and Górniewicz, L., On the Banach contraction principle for multivalued mappings, Approximation, Optimization and Mathematical Economics (Pointe-à-Pitre, 1999), 1-23, Physica, Heidelberg, 2001, https://doi.org/10.1007/978-3-642-57592-1_1 DOI: https://doi.org/10.1007/978-3-642-57592-1_1
Jachymski, J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 194, pp. 293-303, 1995, https://doi.org/10.1006/jmaa.1995.1299 DOI: https://doi.org/10.1006/jmaa.1995.1299
Meir, A. and Keeler, E., A theorem on contraction mappings, J. Math. Anal. Appl., 28, pp. 326-329, 1969, https://doi.org/10.1016/0022-247x(69)90031-6 DOI: https://doi.org/10.1016/0022-247X(69)90031-6
Petruşel, A., (ε,ϕ)-locally contractive multivalued mappings and applications, Studia Univ. Babeş-Bolyai Math., 36, pp. 101-110, 1991.
Petruşel, A., Single-valued and multi-valued Meir-Keeler type operators, Rev. Anal. Numér. Théor. Approx., 30, pp. 75-80, 2001, http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art10
Petruşel, A., Operatorial inclusions, House of the Book of Science, 2002.
Petruşel, A. and Rus, I. A., Dynamics on (Pcl(X),Hd) generated by a finite family of multivalued operators on (X,d), Math. Moravica, 5, pp. 103-110, 2001, https://doi.org/10.5937/matmor0105103p DOI: https://doi.org/10.5937/MatMor0105103P
Rus, I. A., Generalized contractions, Cluj University Press, Cluj-Napoca, 2001.
Rus, I. A. and Rus, B., Dynamics on (Pcp(X),H_{d}) generated by a set of dynamics on (X,d), Studia Univ. Babeş-Bolyai Math., 46, pp. 95-103, 2001.
Xu, H.-K., ε-chainability and fixed points of set-valued mappings in metric spaces, Math. Japonica, 39, pp. 353-356, 1994.
Yamaguti, M., Hata, M. and Kigani, J., Mathematics of Fractals, Translations Math. Monograph, vol. 167, AMS Providence, Rhode Island, 1997, https://doi.org/10.1090/mmono/167 DOI: https://doi.org/10.1090/mmono/167
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