A note about the relation between fixed point theory on cone metric spaces and fixed point theory on metric spaces
Functional Analysis
2011-11-15 v1
Abstract
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].
Keywords
Cite
@article{arxiv.1111.3356,
title = {A note about the relation between fixed point theory on cone metric spaces and fixed point theory on metric spaces},
author = {Ion Olaru},
journal= {arXiv preprint arXiv:1111.3356},
year = {2011}
}
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6 pages