Some sequences supplied by inequalities and their applications

Authors

  • Ştefan M. Şoltuz Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat292-671
Abstract views: 218

Abstract

In order to prove the convergence of Ishikawa and Mann iterations, the convergence of one type of sequences is needed. Our purpose, in this note, is to give a new proof of the convergence for one of them. We also give generalizations for the sequences.

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References

S. Ishikawa, Fixed Points by a New Iteration Method, Proc. Amer. Math. Soc. 44 (1974), 147-150, https://doi.org/10.1090/s0002-9939-1974-0336469-5 DOI: https://doi.org/10.1090/S0002-9939-1974-0336469-5

R. W. Mann, Mean Value Methods in Iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510, https://doi.org/10.1090/s0002-9939-1953-0054846-3 DOI: https://doi.org/10.1090/S0002-9939-1953-0054846-3

J. A. Park, Mann-Iteration for Strictly Pseudocontractive Maps, J. Korean Math. Soc. 31 (1994), 333-337.

H. Y. Zhou, Stable Iteration Procedures for Strong Pseudocontractions and Nonlinear Equations Involving Accretive Operators without Lipschitz Assumption, J. Math. Anal. Appl. 230 (1999), 1-30. DOI: https://doi.org/10.1006/jmaa.1998.6108

H. Y. Zhou, J. Yuting, Approximation of Fixed Points of Strongly Pseudocontractive Maps without Lipschtzian Assumption, Proc. Amer. Math. Soc. 125 (1997), 1705-1709, https://doi.org/10.1090/s0002-9939-97-03850-1 DOI: https://doi.org/10.1090/S0002-9939-97-03850-1

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Published

2000-08-01

How to Cite

Şoltuz, Ştefan M. (2000). Some sequences supplied by inequalities and their applications. Rev. Anal. Numér. Théor. Approx., 29(2), 207–212. https://doi.org/10.33993/jnaat292-671

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