Mathematics – Functional Analysis
Scientific paper
2011-11-14
Mathematics
Functional Analysis
6 pages
Scientific paper
Let Y be a locally convex Hausdorff space, K \subset E a cone and \leq_K the partial order defined by K. Let (X, p) be a TV S- cone metric space, {\phi} : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that p(f(x), f(y)) \leq_K {\phi}(p(x, y)), for all x, y \in X. We shall show that there exists a scalar comparison function {\psi} : R+ \rightarrow R+ and a metric d_p(in usual sense) on X such that d_p(f(x), f(y)) \leq {\psi}(d_p(x, y)), for all x, y \in X. Our results extend the results of Du (2010) [Wei-Shih Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010), 2259-2261].
No associations
LandOfFree
A note about the relation between fixed point theory on cone metric spaces and fixed point theory on metric spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A note about the relation between fixed point theory on cone metric spaces and fixed point theory on metric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A note about the relation between fixed point theory on cone metric spaces and fixed point theory on metric spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-707883