Geodesic
Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 817-826 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 47H04, 47H10, 47J25, 54C60, 54H25
Keywords: multi-valued map; Mann iterates; Ishikawa iterates; fixed points 
@article{CMJ_2005_55_4_a0,
     author = {Sastry, K. P. R. and Babu, G. V. R.},
     title = {Convergence of {Ishikawa} iterates for a multi-valued mapping with a fixed point},
     journal = {Czechoslovak Mathematical Journal},
     pages = {817--826},
     year = {2005},
     volume = {55},
     number = {4},
     mrnumber = {2184365},
     zbl = {1081.47069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a0/}
}
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
SP  - 817
EP  - 826
VL  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a0/
LA  - en
ID  - CMJ_2005_55_4_a0
ER  - 
%0 Journal Article
%A Sastry, K. P. R.
%A Babu, G. V. R.
%T Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point
%J Czechoslovak Mathematical Journal
%D 2005
%P 817-826
%V 55
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a0/
%G en
%F CMJ_2005_55_4_a0
Sastry, K. P. R.; Babu, G. V. R. Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 817-826. http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a0/