" Completion of Cone Metric Spaces and Fixed Point Theory"
Abstract: Fixed point theory occupies a huge place in metric spaces. One of the important questions may arise in this connection is whether metric spaces really provide enough space for this theory or not. Recently, and in Huang L-G and Zhang X., Cone metric spaces and fixed point theorems of contractive mappings , J. Math. Anal. Appl.} 323 (2007), 1468--1476.},the authors there somehow implied that the answer is no. Actually, they introduced the notion of cone metric space, where they gave an example of a function which is contraction in the category of cone metric spaces but not contraction if considered over metric spaces and hence, by proving a fixed point theorem in cone metric spaces, ensured that this map must have a unique fixed point.
After that series of articles about cone metric spaces started to appear. Some of those articles dealt with fixed point theorems in those spaces, specially in complete ones, and some other with the structure of the spaces themselves.
Motivated by this , two completion theorems for cone metric spaces and cone normed spaces are proved. Using the scalar norm of the Banach space containing the cone in defining the completion space, we prefer to call this completion a scalar completion.
Tea and cookies will be served before the seminar.
Date: Wednesday, May 6, 2009
Place: Mathematics Seminar Room, SA-141