## Iterative approximation of fixed points of Lipschitz pseudocontractive maps.(English)Zbl 0979.47038

Let $$E$$ be a $$q$$-uniformly smooth Banach space with a weakly sequentially continuous duality map and $$T$$ be a Lipschitzian pseudocontractive selfmapping of a nonempty closed bounded and assume $$\chi$$ be in $$K$$. The author’s gives an iterative approximation method for a fixed point of $$T$$. If $$E$$ is a Hilbert space the approximation converges to the fixed point closest to $$\chi$$.

### MSC:

 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47J05 Equations involving nonlinear operators (general) 47H10 Fixed-point theorems 47J25 Iterative procedures involving nonlinear operators
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### References:

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