arXiv subjects

Ion Olaru

Publications and source records attributed to Ion Olaru.

3 recordsLinked to original sources

arXiv2012

About nonlinear contractive conditions on cone metric spaces

In the present work we shall show that nonlinear contractive conditions on TVS-cone metric spaces can be reduced to nonlinear contractive conditions on usual metric spaces. Our results extend the results of Du (2010) [W.S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010), 2259-2261] and results of Abdeljawad and Rezapour [T. Abdeljawad, Sh. Rezapour, Some fixed point results in TVS-cone metric spaces, Fixed Point Theory (to appear 2012)].

math.FA↗

arXiv2011

Some common fixed points results on metric spaces over topological modules

In this paper, we replace the real numbers by a topological R-module and define R-metric spaces $(X,d)$. Also, we prove some common fixed point theorems on R-module metric spaces. We obtain, as a particular case the Perov theorem.

math.FA↗

arXiv2011

A note about the relation between fixed point theory on cone metric spaces and fixed point theory on metric spaces

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, ϕ : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that p(f(x), f(y)) \leq_K ϕ(p(x, y)), for all x, y \in X. We shall show that there exists a scalar comparison function ψ : R+ \rightarrow R+ and a metric d_p(in usual sense) on X such that d_p(f(x), f(y)) \leq ψ(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].

math.FA↗