Thesis (Ph. D.), Memorial University of Newfoundland, 1999. / Bibliography: p. 148-150.

In this thesis, we first obtain coincidence and common fixed point theorems for a pair of generalized non-expansive type mappings in a normed space. Then we discuss two types of convergence theorems, namely, the convergence of Mann iteration procedures and the convergence and stability of fixed points. In addition, we discuss the viscosity approximations generated by (ψ ,ϕ)-weakly contractive mappings and a sequence of non-expansive mappings and then establish Browder and Halpern type convergence theorems on Banach spaces. With regard to iteration procedures, we obtain a result on the convergence of Mann iteration for generalized non-expansive type mappings in a Banach space which satisfies Opial's condition. And, in the case of stability of fixed points, we obtain a number of stability results for the sequence of (ψ,ϕ)- weakly contractive mappings and the sequence of their corresponding fixed points in metric and 2-metric spaces. We also present a generalization of Fraser and Nadler type stability theorems in 2-metric spaces involving a sequence of metrics.

An initial study of the delayed coincidence technique and methods of analysis has been made. Three methods of analysis are attempted: the slope, the method of moments and the "unfolding" method. Necessary corrections to minimize errors of calculation are proposed and numerical checks of the methods are performed. Half lives of the levels 829 and 864 keV in ¹¹⁵In were separately measured by means of β-γ delayed coincidence technique. A Ge (Li) detector of 4cc active volume, in conjunction with a constant fraction timing discriminator, was used to detect the γ- branch. The data from this experiment were analysed by the above mentioned methods and the proposed corrections were made. Good correspondence was obtained between the unfolding and the method of moments, while the valµe obtained using the slope method was slightly higher. The numerical test of the analysis methods could not explain this difference completely. It was assumed that the difference was due to fluctuations in the collected data. / Master of Science

The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.