" Completion of Cone Metric Spaces and Fixed Point Theory"

By

**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**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room, SA-141**