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The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings. (English) Zbl 0729.47052
Let C be a nonempty subset of a normed space. An operator T: $$C\to C$$ is called
(i) hemicontractive, if $$\| Tx-p\|^ 2\leq \| x-p\|^ 2+\| x-Tx\|^ 2$$ for $$x\in C$$ and $$p\in Fix(T);$$
(ii) generalized contractive, if $$\| Tx-Ty\| <\max \{\| x- y\|$$, $$\| x-Tx\|$$, $$\| y-Ty\|$$, $$\| x-Ty\|$$, $$\| y-Tx\| \}$$ for x,y$$\in C$$, $$x\neq y.$$
The author proves theorems on convergence of the sequence of Ishikawa iterates in the case where T is continuously mapping a compact and convex subset C of a Hilbert space into itself, and satisfied either (i) or (ii).

##### MSC:
 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47J25 Iterative procedures involving nonlinear operators
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##### References:
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