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Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Paolamaria Pietramala (1991)

Commentationes Mathematicae Universitatis Carolinae

Let K be a closed convex subset of a Hilbert space H and T : K K a nonexpansive multivalued map with a unique fixed point z such that { z } = T ( z ) . It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to z .

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

K. P. R. Sastry, G. V. R. Babu (2005)

Czechoslovak Mathematical Journal

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...

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