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The Equivalence between the Mann and Ishikawa Iterations for Generalized Contraction Mappings in a Cone

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DOI: 10.4236/am.2011.211192    3,799 Downloads   6,777 Views   Citations

ABSTRACT

In this paper, equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. Doss and T. Esakkiappan, "The Equivalence between the Mann and Ishikawa Iterations for Generalized Contraction Mappings in a Cone," Applied Mathematics, Vol. 2 No. 11, 2011, pp. 1369-1371. doi: 10.4236/am.2011.211192.

References

[1] W. R. Mann, “Mean Value Methods in Iteration,” Proceedings of the American Mathematical Society, Vol. 4, No. 3, 1953, pp. 506-510. doi:10.1090/S0002-9939-1953-0054846-3
[2] S. Ishikawa, “Fixed Points by a New Iteration Method,” Proceedings of the American Mathematical Society, Vol. 44, No. 1, 1974, pp. 147-150. doi:10.1090/S0002-9939-1974-0336469-5
[3] L.-G. Huang and X. Zhang, “Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings,” Journal of Mathematical Analysis and Applications, Vol. 332, No. 2, 2007, pp.1468-1476. doi:10.1016/j.jmaa.2005.03.087
[4] X. Weng, “Fixed Point Iteration for Local Strictly Pseudo-Contractive Mapping,” Proceedings of the American Mathematical Society, Vol. 113, No. 3, 1991, pp. 727-731. doi:10.1090/S0002-9939-1991-1086345-8
[5] B. E. Rhoades, “Convergence of an Isikawa-Type Iteration Scheme for a Generalized Contraction,” Journal of Mathematical Analysis and Applications, Vol. 185, No. 2, 1994, pp. 350-355. doi:10.1006/jmaa.1994.1253
[6] B. E. Rhoades and S. M. Soltuz, “The Eqivalence between Mann and Ishikawa Iterations Dealing with Generalized Contractions,” International Journal of Mathematics and Mathematical Sciences, Vol. 2006, 2006, pp. 1-5.

  
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