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

Title:

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

Creator:

Sastry, K. P. R. and Babu, G. V. R.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:160fdafb-c495-4347-aa31-b2bedf380ed0
uuid:160fdafb-c495-4347-aa31-b2bedf380ed0

Subject:

multi-valued map, Mann iterates, Ishikawa iterates, and fixed points

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

817-826

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:4

Harvested from:

CDK

Metadata only:

false