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Iterative approximation of fixed points of Lipschitz pseudocontractive maps |
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| Authors: | C E Chidume |
| Institution: | The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586, Trieste, Italy |
| Abstract: | Let |
| Keywords: | Pseudocontractive operators $q$-uniformly smooth spaces duality maps weak sequential continuity |
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be a 
-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., 
). Let 
be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset 
of 
and let 
be arbitrary. Then the iteration sequence 
defined by 
, converges strongly to a fixed point of 
, provided that 
and 
have certain properties. If 
is a Hilbert space, then 
converges strongly to the unique fixed point of 
closest to 
.