Search results for "cone metric space"
showing 10 items of 25 documents
MR2684111 Kadelburg, Zoran; Radenović, Stojan; Rakočević, Vladimir Topological vector space-valued cone metric spaces and fixed point theorems. Fixed…
2011
Recently, Huang and Zhang [\emph{Cone metric spaces and fixed point theorems of contractive mappings}, J. Math. Anal. Appl., \textbf{332} (2007), 1468 -1476] defined cone metric spaces by substituing an order normed space for the real numbers and proved some fixed point theorems. Let $E$ be a real Hausdorff topological vector space and $P$ a cone in $E$ with int\,$P\neq \emptyset$, where int\,$P$ denotes the interior of $P$. Let $X$ be a nonempty set. A function $d : X \times X\to E$ is called a \emph{tvs}-cone metric and $(X, d)$ is called a \emph{tvs}-cone metric space, if the following conditions hold: (1) $\theta \leq d(x, y)$ for all $x, y \in X$ and $d(x, y)= \theta$ if and only if $x…
Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces
2013
Abstract In this paper, we prove some fixed point theorems for generalized contractions in the setting of G -metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74–79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317]. We prove, also, a fixed point theorem in the setting of G -cone metric spaces.
Some critical remarks on the paper “A note on the metrizability of tvs-cone metric spaces” / Некоторые критические замечания о работе «Заметки о метр…
2018
This short and concise note provides a detailed exposition of the approach and results established by (Lin et al, 2015, pp.271-279). We show that the obtained results are not particularly surprising and new. Namely, using an old result due to K. Deimling it is indicated that tvs-cone metric spaces over solid cones are actually cone metric spaces over normal solid cones. Hence, there are only cone metric spaces over normal solid cones or over normal non-solid cones. One question still unanswered is whether an ordered topological vector space with a non-normal non-solid cone exists. / В представленных, в данной статье, заметках приведен подробный обзор методов и полученных результатов исследо…
Nonlinear quasi-contractions of Ciric type
2012
In this paper we obtain points of coincidence and common fixed points for two self mappings satisfying a nonlinear contractive condition of Ciric type. As application, using the scalarization method of Du, we deduce a result of common fixed point in cone metric spaces.
Fixed point results on metric-type spaces
2014
Abstract In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.
Common fixed points for self mappings on compact metric spaces
2013
In this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of Suzuki type. We also present some examples to illustrate our results. Moreover, using the scalarization method of Du, we deduce a result of common fixed point in compact cone metric spaces.
Common fixed points in cone metric spaces for $MK$-pairs and $L$-pairs
2011
In this paper we introduce some contractive conditions of Meir-Keeler type for a pair of mappings, called $MK$-$pair$ and $L\textrm{-}pair$, in the framework of cone metric spaces and we prove theorems which assure existence and uniqueness of common fixed points for $MK$-$pairs$ and $L \textrm{-}pairs$. As an application we obtain a result of common fixed point of a $p$-$MK$-pair, a mapping and a multifunction, in complete cone metric spaces. These results extend and generalize well-known comparable results in the literature.
MR2670689 Rezapour, Shahram; Khandani, Hassan; Vaezpour, Seyyed M. Efficacy of cones on topological vector spaces and application to common fixed poi…
2011
Recently, Huang and Zhang defined cone metric spaces by substituting an order normed space for the real numbers and proved some fixed point theorems. For fixed point results in the framework of cone metric space see, also, Di Bari and Vetro [\textit{$\varphi$-pairs and common fixed points in cone metric spaces}, Rend. Circ. Mat. Palermo \textbf{57} (2008), 279--285 and \textit{Weakly $\varphi$-pairs and common fixed points in cone metric spaces}, Rend. Circ. Mat. Palermo \textbf{58} (2009), 125--132]. Let $(E,\tau)$ be a topological vector space and $P$ a cone in $E$ with int\,$P\neq \emptyset$, where int\,$P$ denotes the interior of $P$. The authors define a topology $\tau_p$ on $E$ so tha…
$varphi$-pairs and common fixed points in cone metric spaces
2008
In this paper we introduce a contractive condition, called $\varphi \textrm{-}pair$, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for $\varphi \textrm{-}pairs$. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.
Weakly \varphi-pairs and common fixed points in cone metric spaces
2009
In this paper we introduce a weak contractive condition, called weakly \varphi-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.