Remarks about an inequality used for the equivalence between the convergence of Ishikawa and Mann iterations

Authors

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

DOI:

https://doi.org/10.33993/jnaat362-867

Keywords:

modified Ishikawa iterations, modified Mann iterations, asymptotically pseudocontractive map
Abstract views: 230

Abstract

We prove an inequality which is crucial in the proof of the main result from B.E. Rhoades and ?tefan M. ?oltuz, The Equivalence between the Convergences of Ishikawa and Mann Iterations for an Asymptotically Pseudocontractive Map, J. Math. Anal. Appl., 283 (2003), 681-688.

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References

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 DOI: https://doi.org/10.1090/S0002-9939-1974-0336469-5

Kato, T., Nonlinear Semigroup and Evolution Equations, J. Math. Soc. Japan, 19, pp. 508-520, 1967, https://doi.org/10.2969/jmsj/01940508 DOI: https://doi.org/10.2969/jmsj/01940508

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 DOI: https://doi.org/10.1090/S0002-9939-1953-0054846-3

Rhoades, B. E. and Şoltuz, Ş. M., The equivalence between the convergences of Ishikawa and Mann iterations for asymptotically pseudocontractive map, J. Math. Anal. Appl., 283, pp. 681-688, 2003, https://doi.org/10.1016/s0022-247x(03)00338-x DOI: https://doi.org/10.1016/S0022-247X(03)00338-X

Schu, J., Iterative Construction of Fixed Points of Asymptotically Nonexpansive Mappings, J. Math. Anal. Appl., 158, pp. 407-413, 1991, https://doi.org/10.1016/0022-247x(91)90245-u DOI: https://doi.org/10.1016/0022-247X(91)90245-U

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Published

2007-08-01

How to Cite

Şoltuz, Ştefan M. (2007). Remarks about an inequality used for the equivalence between the convergence of Ishikawa and Mann iterations. Rev. Anal. Numér. Théor. Approx., 36(2), 187–191. https://doi.org/10.33993/jnaat362-867

Issue

Vol. 36 No. 2 (2007)

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Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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