Comparing Krasnoselskij and Mann Iterative Methods for Lipschitzian Generalized Pseudo-Contractive Operators in Hilbert Spaces
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Date
2009-08-12
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Abstract
We introduce certain iterative methods (Krasnoselskij, Mann and Ishikawa) that ensure convergence to a fixed point for certain classes of operators that satisfy weak contractive type conditions, for which the Picard iteration guarantees no convergence. Some convergence theorems are stated and proved for these classes of operators.
We finally compare the convergence rate of Krasnoselskij and Mann iterative methods known to converge to a fixed point of Lipschitzian generalized pseudo-contractive operators in Hilbert spaces.
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A Thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology
in partial fulfillment of the requirements for the degree of Master of Science in Mathematics.