Approximation methods for common fixed points of non-expansive mappings in Hilbert spaces
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Date
October 11, 2016
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Abstract
This thesis is an extensive exposition and review of the paper "Approximation methods of
common fixed point of non-expansive mappings in a Hilbert space" in which the author, Paul-
Emile Mainge proposed two numerical approaches to solving this problem by implicit and
explicit viscosity like-methods. The study as obtain in the thesis was the strong convergence
results of the implicit anchor-like algorithm and the explicit procedure for approximating the
common fixed point of countable infinite family of non-expansive self-mappings. This thesis
basically details the proofs of the main theorem of Paul’s paper as well as detailed exposition
of the mathematics involved in it. Detailed proofs of subsidiary results leading up to the proof
of the main theorem of Paul’s paper are also discussed. Finally, the main theorem of the paper
is also demonstrated in a series of lemmas.
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the degree of Master of Philosophy in Pure Mathematics.