Fixed point theorems for n -periodic mappings in Banach spaces

Jarosław Górnicki; Krzysztof Pupka

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 33-42
  • ISSN: 0010-2628

Abstract

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Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. 29 (1971), 294) and others, which have recently been presented in Chapter 11 of Handbook of Metric Fixed Point Theory (2001).

How to cite

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Górnicki, Jarosław, and Pupka, Krzysztof. "Fixed point theorems for $n$-periodic mappings in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 33-42. <http://eudml.org/doc/249561>.

@article{Górnicki2005,
abstract = {Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. 29 (1971), 294) and others, which have recently been presented in Chapter 11 of Handbook of Metric Fixed Point Theory (2001).},
author = {Górnicki, Jarosław, Pupka, Krzysztof},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {lipchitzian mapping; uniformly lipschitzian mapping; $n$-periodic mapping; fixed point; Lipschitzian mapping; uniformly Lipschitzian mapping},
language = {eng},
number = {1},
pages = {33-42},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fixed point theorems for $n$-periodic mappings in Banach spaces},
url = {http://eudml.org/doc/249561},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Górnicki, Jarosław
AU - Pupka, Krzysztof
TI - Fixed point theorems for $n$-periodic mappings in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 33
EP - 42
AB - Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. 29 (1971), 294) and others, which have recently been presented in Chapter 11 of Handbook of Metric Fixed Point Theory (2001).
LA - eng
KW - lipchitzian mapping; uniformly lipschitzian mapping; $n$-periodic mapping; fixed point; Lipschitzian mapping; uniformly Lipschitzian mapping
UR - http://eudml.org/doc/249561
ER -

References

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  1. Goebel K., Convexity of balls and fixed point theorems for mappings with nonexpansive square, Compositio Math. 22 (1970), 269-274. (1970) Zbl0202.12802MR0273477
  2. Goebel K., Kirk W.A., A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973), 135-140. (1973) Zbl0265.47044MR0336468
  3. Goebel K., Złotkiewicz E., Some fixed point theorems in Banach spaces, Colloquium Math. 23 (1971), 103-106. (1971) MR0303367
  4. Górnicki J., Fixed points of involutions, Math. Japonica 43 1 (1996), 151-155. (1996) MR1373993
  5. Halpern B., Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967), 957-961. (1967) MR0218938
  6. Kim T.H., Kirk W.A., Fixed point theorems for lipschitzian mappings in Banach spaces, Nonlinear Anal. 26 (1996), 1905-1911. (1996) Zbl0856.47031MR1386122
  7. Kirk W.A., A fixed point theorem for mappings with a nonexpansive iterate, Proc. Amer. Math. Soc. 29 (1971), 294-298. (1971) Zbl0213.41303MR0284887
  8. Kirk W.A., Sims B. (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Pub., Dordrecht-Boston-London, 2001. Zbl0970.54001MR1904271
  9. Linhart J., Fixpunkte von Involutionen n-ter Ordnung, Österreich. Akad., Wiss. Math.-Natur., kl. II, 180 (1973), 89-93. Zbl0244.47041MR0303369

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