Self-similar sets in convex metric spaces

Authors

  • Ghiocel Moţ “Aurel Vlaicu” University, Ara, Romania

DOI:

https://doi.org/10.33993/jnaat332-776

Keywords:

self-similar set, generalized contraction, convex metric space
Abstract views: 190

Abstract

The purpose of this paper is to present some existence and uniqueness results for self-similar sets in convex complete metric spaces.

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References

Dugundji, J. and Granas, A., Fixed point theory, P. W. N. Warszawa, 1982.

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

Matkowski, J. and Wegrzyk, R., On equivalence of some fixed point theorems for self mappings of metrically convex space, Boll. U. M. I., 15-A, pp. 359-369, 1978.

Moţ, G., Tipuri de convexitate în matematica modernă. Aplicaţii ale teoriei alurii, Editura Mirton, Timişoara, 1999 (in Romanian).

Nadler, S. B., Jr., Multivalued contraction mappings, Pacific J. Math., 30, pp.475-488, 1969, https://doi.org/10.2140/pjm.1969.30.475 DOI: https://doi.org/10.2140/pjm.1969.30.475

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., Dynamical systems, fixed points and fractals, Pure Math. Appl., 13, pp. 275-281, 2002.

Petruşel, A., Multi-funcţii şi aplicaţii, Cluj University Press, Cluj-Napoca, 2001 (in Romanian).

Petruşel, A., Operatorial inclusions, House of the Book of Science, Cluj-Napoca, 2002.

Rus, I. A., Generalized contractions, Cluj University Press, Cluj-Napoca, 2001.

Wegrzyk, R., Fixed point theorems for multivalued functions and their applications to functional equations, Dissertationes Math., 201, pp. 1-30, 1986.

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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Published

2004-08-01

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Articles

How to Cite

Moţ, G. (2004). Self-similar sets in convex metric spaces. Rev. Anal. Numér. Théor. Approx., 33(2), 197-201. https://doi.org/10.33993/jnaat332-776