An Iterated Function System for Reich Contraction in Complete b Metric Space

In this paper, we introduce R Iterated Function System
and employ the Hutchinson Barnsley theory (HB) to construct a
fractal set as its unique fixed point by using Reich contractions in a
complete b metric space. We discuss about well posedness of fixed
point problem for b metric space.

• R. Uthayakumar
• G. Arockia Prabakar

• Fractals
• Iterated Function System
• Compact set
• Reich Contraction
• Well posedness.

[1] B.B.Mandelbrot, The Fractal Geometry of Nature, Freeman New York
(1982).
[2] Crownover and M Richard, Introduction to Fractals and chaos Jones and
Bartlett Publishers London (1995).
[3] J E Hutchinson, Fractals and self similarity, Indiana Univ Math J 30:
(1981)713-47.
[4] Michael F Barnsley, Fractals everywhere, New York: Academic Press
(1993).
[5] Adrian Petrusel, Fixed point theory with applications to Dynamical
Systems and Fractals, Seminar on Fixed point theory (2002) 305-316 .
[6] S.L.Singh, Bhagwati Prasad and Ashish Kumar, Fractals via iterated
functions and multifunctions, Chaos Solitons & Fractals 39 (2009)1224-
1231.
[7] D.R.Sahu, Anindita Chakraborthy and R.P.Dubey, K Iterated Function
System, Fractals 18(1) (2010) 139-144 .
[8] D. Easwaramoorthy and R. Uthayakumar. Analysis on Fractals in Fuzzy
Metric Spaces, Fractals 19:3 (2011) 379-386 .
[9] S.Banach, Sur les opeartions dans les ensembles abstrait et leur application
aux equations, integrals, Fundam.Math. 3 (1922)133-181 .
[10] I.A.Bakhtin, The contraction mapping in almost metric spaces,
Funct.Ana. Gos.Ped.Inst.Unianowsk, 30 (1989) 26-37.
[11] S.Czerwik, Nonlinear Set valued contraction mappings in b metric
spaces, Atti Sem. Mat.Univ.Modena, 46 (1998) 263-276 .
[12] S.L.Singh and Bhagwati Prasad, Some coincidence theorems and stability
of iterative procedures, Computers and Mathematics with Applications
55 (2008) 25122520
[13] S.Reich, Some Remarks concerning contraction mappings,
Canad.Math.Bull 14 (1971) 121-124.
[14] F.S.De Blasi and J.Myjak, Sur la porosite des contractions sans point
fixe, C.R.Acad. Sci. Paris. 308 (1989) 51-54.
[15] S.Reich and A.J.Zaslavski, Well posedness of Fixed point problems,
Far East J. Math. Sci. Special Volume Part III (2001) 393-401.