Abstracts Category : Other

Approximation methods for common fixed points of non-expansive mappings in Hilbert spaces

by Joseph Frank Gordon

This thesis is an extensive exposition and review of the paper "Approximation methods ofcommon 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 andexplicit viscosity like-methods. The study as obtain in the thesis was the strong convergenceresults of the implicit anchor-like algorithm and the explicit procedure for approximating thecommon fixed point of countable infinite family of non-expansive self-mappings. This thesisbasically details the proofs of the main theorem of Pauls paper as well as detailed expositionof the mathematics involved in it. Detailed proofs of subsidiary results leading up to the proofof the main theorem of Pauls paper are also discussed. Finally, the main theorem of the paperis also demonstrated in a series of lemmas. A thesis submitted to the Department of Mathematics,Kwame Nkrumah University of Science and Technology Inpartial fulfillment of the requirement for the Degree of Master of Philosophy in Pure Mathematics, 2016 KNUST