Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point

K. P. R. Sastry; G. V. R. Babu

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 817-826
  • ISSN: 0011-4642

Abstract

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Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map T with a fixed point p and prove that these iterates converge to a fixed point q of T under certain conditions. This fixed point q may be different from p . To illustrate this phenomenon, an example is given.

How to cite

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Sastry, K. P. R., and Babu, G. V. R.. "Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point." Czechoslovak Mathematical Journal 55.4 (2005): 817-826. <http://eudml.org/doc/30991>.

@article{Sastry2005,
abstract = {Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map $T$ with a fixed point $p$ and prove that these iterates converge to a fixed point $q$ of $T$ under certain conditions. This fixed point $q$ may be different from $p$. To illustrate this phenomenon, an example is given.},
author = {Sastry, K. P. R., Babu, G. V. R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {multi-valued map; Mann iterates; Ishikawa iterates; fixed points; multi-valued map; Mann iterates; Ishikawa iterates; fixed points},
language = {eng},
number = {4},
pages = {817-826},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point},
url = {http://eudml.org/doc/30991},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Sastry, K. P. R.
AU - Babu, G. V. R.
TI - Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 817
EP - 826
AB - Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map $T$ with a fixed point $p$ and prove that these iterates converge to a fixed point $q$ of $T$ under certain conditions. This fixed point $q$ may be different from $p$. To illustrate this phenomenon, an example is given.
LA - eng
KW - multi-valued map; Mann iterates; Ishikawa iterates; fixed points; multi-valued map; Mann iterates; Ishikawa iterates; fixed points
UR - http://eudml.org/doc/30991
ER -

References

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