Classical results via Mann-Ishikawa iteration

Authors

  • Ştefan M. Şoltuz Universidad de los Andes, Colombia, and Tiberiu Popoviciu Institute of Numerical Analysis, Romania
  • Diana Otrocol Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords:

delay differential equationș Mann iteration, Ishikawa iteration

Abstract

New proofs of existence and uniqueness results for the solution of the Cauchy problem with delay are obtained by use of Mann-Ishikawa iteration.

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References

Coman, Gh., Pavel, G., Rus, I. and Rus, I. A., Introduction in the theory of operatorial equation, Ed. Dacia, Cluj-Napoca, 1976 (in Romanian).

Hartman, P., Ordinary differential equations, John Wiley & Sons, Inc., New York, London, Sydney, 1964.

Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44, pp. 147-150, 1974, https://doi.org/10.1090/s0002-9939-1974-0336469-5

Mann, W. R., Mean value in iteration, Proc. Amer. Math. Soc., 4, pp. 506-510, 1953, https://doi.org/10.1090/s0002-9939-1953-0054846-3.

Otrocol, D., Data dependence for the solution of a Lotka-Volterra system with two delays, Mathematica, Tome 48 (71), 1, pp. 61-68, 2006.

Rus, I. A., Principles and applications of the fixed point theory, Ed. Dacia, Cluj Napoca, 1979 (in Romanian).

Şoltuz, Ş. M., The equivalence of Picard, Mann and Ishikawa iteration dealing with quasi-contractive operators, Math. Comm. 10, pp. 81-88, 2005.

Şoltuz, Ş. M., An equivalence between the convergence of Ishikawa, Mann and Picard iterations, Math. Comm. 8, pp. 15-22, 2003.

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Published

2007-08-01

How to Cite

Şoltuz, Ştefan M., & Otrocol, D. (2007). Classical results via Mann-Ishikawa iteration. Rev. Anal. Numér. Théor. Approx., 36(2), 193–197. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art8

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