Extending the collage theorem to contractive like operators
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https://doi.org/10.33993/jnaat382-913Keywords:
contractive like operatorsAbstract
We generalize the classical "collage'' theorem, due to Barnsley, to contractive like operators.Downloads
References
Barnsley, M. F., Fractals everywhere, New York: Academic Press, 1988.
Berinde, V., On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Math. Univ. Comenianae, Vol. LXXIII, no. 1, pp. 119-126, 2004. DOI: https://doi.org/10.1155/S1687182004311058
Berinde, V., Iterative approximation of fixed points, Springer-Verlag Berlin Heidelberg, 2007. DOI: https://doi.org/10.1109/SYNASC.2007.49
Imoru C.O. and Olatiwo, M.O., On the stability of Picard and Mann iteration processes, Carpathian J. Math., 19, pp. 155-160, 2003.
Kunze H.E. and Vrscay, E.R. Solving inverse problems for ordinary differential equations using the Picard contraction mapping, Inverse Problems, 15, pp. 745-770, 1999, https://doi.org/10.1088/0266-5611/15/3/308 DOI: https://doi.org/10.1088/0266-5611/15/3/308
Kunze, H.E. and Gomes, S., Solving an inverse problem for Urison-type integral equations using Banach's fixed point theorem, Inverse Problems, 19, pp. 411-418, 2003, https://doi.org/10.1088/0266-5611/19/2/310 DOI: https://doi.org/10.1088/0266-5611/19/2/310
Kunze, H.E., Hicken, J.E and Vrscay, E.R., Inverse problems for ODEs using contraction maps and suboptimality for the `collage method', Inverse Problems, 20, 2004, https://doi.org/10.1088/0266-5611/20/3/019 DOI: https://doi.org/10.1088/0266-5611/20/3/019
Osilike, M.O., Stability results for fixed point iteration procedures, J. Nigerian Math. Soc., 14/15, pp. 17-29, 1995/96.
Osilike, M.O., Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math., 28, no. 9, pp. 1251-1265, 1997.
Rhoades, B.E., Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc., 196, pp. 161-176, 1974, https://doi.org/10.1090/s0002-9947-1974-0348565-1 DOI: https://doi.org/10.1090/S0002-9947-1974-0348565-1
Şoltuz, Ş. M., Solving inverse problems via hemicontractive maps, Nonlinear Analysis, 71, pp. 2387-2390, 2009, https://doi.org/10.1016/j.na.2009.01.071 DOI: https://doi.org/10.1016/j.na.2009.01.071
Şoltuz, S. M., Solving inverse problems via weak-contractive maps, Rev. Anal. Numer. Theor. Approx., 37, No. 2, pp. 217-220, 2008, http://ictp.acad.ro/jnaat/journal/article/view/2008-vol37-no2-art14
Zamfirescu, T., Fixed Point Theorems in metric spaces, Arch. Math., 23, pp. 292-298, 1972. DOI: https://doi.org/10.1007/BF01304884
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