Generalized projection and approximation of fixed points of nonself maps |
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Authors: | C E Chidume M Khumalo H Zegeye |
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Institution: | a The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586 Strada Costiera, Trieste 11-34014, Italy;b University of Swaziland, Kwaluseni, Swaziland |
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Abstract: | Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established. |
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Keywords: | Asymptotically weakly suppressive Asymptotically nonextensive Asymptotically weakly contractive Generalized projection Uniformly convex and uniformly smooth Banach spaces |
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