Generalized Iterated Function Systems Containing Functions of Integral Type

Authors

  • Minirani S
  • . .

DOI:

https://doi.org/10.14419/ijet.v7i3.31.18280

Published:

2018-08-24

Keywords:

attractor, fixed point, generalized iterated function system, integral type contractions, product space.

Abstract

A finite collection of mappings which are contractions on a complete metric space constitutes an iterated function system. In this paper we study the generalized iterated function system which contain generalized contractions of integral type from the product space . We prove the existence and uniqueness of the fixed point of such an iterated function system which is also known as its attractor.

 

References

[1] A. Branciari (2002), A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29(9), pp. 531-536.

[2] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, (1982).

[3] D. Dumitru (2009), Generalised iterated function systems containing Meir-Keeler functions, An. Univ. Bucuresti. math. LVIII, pp. 3-15.

[4] J. E. Hutchinson (1981), Fractals and self similarity, Indiana Univ. Math. J. 30, pp. 713-747.

[5] K. J. Falconer, Fractal Geometry - Mathematical foundations and applications, John Wiley Sons, (1990).

[6] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, (1985).

[7] M. F. Barnsley, Fractals Everywhere, Academic Press, Boston, MA, (1988).

[8] S. Minirani (2017), Fixed points of iterated function systems of integral type, (Under review).

[9] S. Minirani (2018), Fixed point of iterate function system containing Meir Keeler integral type contractions, Mathematical Sciences International Research Journal, 7 (1), pp. 391-395.

[10] R. Miculescu and A. Mihail (2016), Reich-type iterated function systems, J. Fixed Point Theory Appl., 18, pp. 285-296.

[11] R. Miculescu and A. Mihail (2008), R. Vrscay, Applications of fixed point theorems in the theory of generalized IFS, Fixed Point Theory Appl., 2, article ID 312876.

[12] N. A. Secelean (2001), Countable iterated function systems, Far East J. Dyn. Syst., 3, pp. 149-167.

[13] S. Banach (1922), Sur les operations dans les ensembles abstrait et leur application aux equations, integrals, Fundam. math., 3, pp. 133-181.

View Full Article:

How to Cite

S, M., & ., . (2018). Generalized Iterated Function Systems Containing Functions of Integral Type. International Journal of Engineering & Technology, 7(3.31), 126–128. https://doi.org/10.14419/ijet.v7i3.31.18280
Received 2018-08-25
Accepted 2018-08-25
Published 2018-08-24