On the convergence of the Ishikawa iterates to a common fixed point of two mappings

Ljubomir B. Ćirić; Jeong Sheok Ume; M. S. Khan

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 2, page 123-127
  • ISSN: 0044-8753

Abstract

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Let C be a convex subset of a complete convex metric space X , and S and T be two selfmappings on C . In this paper it is shown that if the sequence of Ishikawa iterations associated with S and T converges, then its limit point is the common fixed point of S and T . This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].

How to cite

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Ćirić, Ljubomir B., Ume, Jeong Sheok, and Khan, M. S.. "On the convergence of the Ishikawa iterates to a common fixed point of two mappings." Archivum Mathematicum 039.2 (2003): 123-127. <http://eudml.org/doc/249128>.

@article{Ćirić2003,
abstract = {Let $C$ be a convex subset of a complete convex metric space $X$, and $S$ and $T$ be two selfmappings on $C$. In this paper it is shown that if the sequence of Ishikawa iterations associated with $S$ and $T$ converges, then its limit point is the common fixed point of $S$ and $T$. This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].},
author = {Ćirić, Ljubomir B., Ume, Jeong Sheok, Khan, M. S.},
journal = {Archivum Mathematicum},
keywords = {Ishikawa iterates; comon fixed point; convex metric space; metric space; convex structure},
language = {eng},
number = {2},
pages = {123-127},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the convergence of the Ishikawa iterates to a common fixed point of two mappings},
url = {http://eudml.org/doc/249128},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Ćirić, Ljubomir B.
AU - Ume, Jeong Sheok
AU - Khan, M. S.
TI - On the convergence of the Ishikawa iterates to a common fixed point of two mappings
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 2
SP - 123
EP - 127
AB - Let $C$ be a convex subset of a complete convex metric space $X$, and $S$ and $T$ be two selfmappings on $C$. In this paper it is shown that if the sequence of Ishikawa iterations associated with $S$ and $T$ converges, then its limit point is the common fixed point of $S$ and $T$. This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].
LA - eng
KW - Ishikawa iterates; comon fixed point; convex metric space; metric space; convex structure
UR - http://eudml.org/doc/249128
ER -

References

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  7. Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc. 196 (1974), 161–176. Zbl0422.90089MR0348565
  8. A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257–290. Zbl0394.54026MR0433430
  9. Extension of some fixed point theorems of Ćirić, Maiti and Pal, Math. Sem. Notes Kobe Univ. 6 (1978), 41–46. MR0494051
  10. Comments on two fixed point iteration methods, J. Math. Anal. Appl. 56 (1976), 741–750. Zbl0353.47029MR0430880
  11. Fixed point iteration using infinite matrices, In “Applied Nonlinear Analysis” (V. Lakshmikantham, Ed.), pp.689–703, Academic Press, New York, 1979. MR0537576
  12. Generalized contractions and the sequence of iterates, In “Nonlinear Equations in Abstract Spaces” (V. Lakshmikantham, Ed.), pp. 439–462, Academic Press, New York, 1978. MR0502557
  13. A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970), 142–149. MR0267565

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