Research Article
Article:Non Linear Dynamics of Ishikawa Iteration
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 7 - Issue 13 |
| Published: October 2010 |
| Authors: Yashwant S Chauhan, Rajeshri Rana, Ashish Negi |
10.5120/1320-1674
|
Yashwant S Chauhan, Rajeshri Rana, Ashish Negi . Article:Non Linear Dynamics of Ishikawa Iteration. International Journal of Computer Applications. 7, 13 (October 2010), 43-49. DOI=10.5120/1320-1674
@article{ 10.5120/1320-1674,
author = { Yashwant S Chauhan,Rajeshri Rana,Ashish Negi },
title = { Article:Non Linear Dynamics of Ishikawa Iteration },
journal = { International Journal of Computer Applications },
year = { 2010 },
volume = { 7 },
number = { 13 },
pages = { 43-49 },
doi = { 10.5120/1320-1674 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2010
%A Yashwant S Chauhan
%A Rajeshri Rana
%A Ashish Negi
%T Article:Non Linear Dynamics of Ishikawa Iteration%T
%J International Journal of Computer Applications
%V 7
%N 13
%P 43-49
%R 10.5120/1320-1674
%I Foundation of Computer Science (FCS), NY, USA
Abstract
We introduce in this paper the dynamics for Ishikawa iteration procedure. The geometry of Relative Superior Mandelbrot sets are explored for Ishikawa iterates.
References
- R.Abraham and C.Shaw, Dynamics: “The Geometry of Behaviour, Part One: Periodic Behavior, Part Two: Chaotic Behavior”, Aerial Press, Santa Cruz, Calif, (1982).
- Alan F.Beardon, “Iteration of Rational functions”, Springer Verlag, N.York, Inc.(1991).
- V.Berinde, “Iterative approximation of fixed points”, Editura Efermeide, Baia Mare, (2002).
- S,Beddings and K.Briggs, “Itreation of quaterinian maps”, Int J. Bifur Chaos. Appl. Sci. and Engg.5 (1995), 877-881.
- B.Branner and J.Hubbard, “The Iteration of Cubic Polynomials”. Part I,Acta. Math. 66(1998), 143-206.
- G.V.R.Babu and K.N.V.Prasad, “Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators”, Fixed Point Theory and its Applications, Vol. 2006, Art. ID 49615, 1-6(2006).
- P.W.Carlson, “Pseudo 3D rendering methods for fractals in the complex plane, Computer and Graphics”, 20(5), (1996), 757-758.
- R.M.Crownover, “Introduction to Fractals and Chaos, Mandelbrot sets”, Jones and Barlett Publishers, (1995).
- R.L.Daveney, “An Introduction to Chaotic Dynamical Systems”, Springer–Verlag, N.York.Inc.1994.
- K.Heinz, Becker and Michael Dorfler, “Dynamical Systems and Fractals”, Cambridge Univ. Press, 1989.
- R.A.Hohngren, “A First Course in Discrete Dynamical Systems”, Springer–Verlag, 1994.
- S.Ishikawa, “Fixed points by a new iteration method”, Proc. Amer. Math. Soc.44 (1974), 147-150.
- M.A.Kransnosel, “Two remarks on method of successive approximations”, Uspehi. Math. Nauk. 10(1995), 123-127.
- W.R.Mann, “Mean Value methods in iteration”, Proc. Amer. Math. Soc.4 (1953), 506-510.
- B.B.Mandelbrot, “The Fractal aspects of iteration of for complex and z,” Ann. N. Y. Acad. Sci. 357(1980), 249-259.
- J.R.Munkers, “Topology: A First course “, Prantice Hall of India Publ. Ltd., N.Delhi, 1988.
- M.O.Osilike, “Stability results for Ishikawa fixed point iteration procedure”, Indian Journal of Pure and Appl. Math., 26(1995), 937-945.
- M.O.Osilike, “Iterative construction of fixed points of multivalued operators of the accretive type”, Sochow J.Math. 22(1996), 85-92.
- H.Peitgen, H.Jurgens and D.Saupe, “Fractals for classroom Part Two, Complex Systems AND Mandelbrot Sets”, Springer-Verlag, N.York, Inc. 1992.
- H.Peitgen, H.Jurgens and D.Saupe,” Chaos and Fractals”, Springer-Verlag, N.York, Inc. 1992.
- M.Rani and V.Kumar, “Superior Mandelbrot Set”, J Korea Soc. Math. Edu. Series, DResearch in Maths. Edu. no.4,8(2004), 279-291.
- B.E.Rhoades, “Some fixed point iterations procedures”, Int.J.Math.Sci. 14(1991), 1-16.
- B.E.Rhoades, “Fixed points iterations for certain nonlinear mappings”, J .Math. Anal. Appl., 183(1994), 118-120.
- B.E.Rhoades and S.M.Solutz, “On the equivalence of Mann and Ishikawa iteration methods”, Int J. Math. Sci. no.7 (2003), 451-459.
- D.Rochon, “A Generalized Mandelbrot Set for Bi-Complex Numbers”, World Scientific Publishing Company, Fractals 8(4), (2000), 355-368.
Index Terms
Keywords