Search results for " common fixed point"
showing 10 items of 19 documents
Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces
2011
We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.
Coupled common fixed point theorems in partially ordered G-metric spaces for nonlinear contractions
2014
The aim of this paper is to prove coupled coincidence and coupled common fixed point theorems for a mixed $g$-monotone mapping satisfying nonlinear contractive conditions in the setting of partially ordered $G$-metric spaces. Present theorems are true generalizations of the recent results of Choudhury and Maity [Math. Comput. Modelling 54 (2011), 73-79], and Luong and Thuan [Math. Comput. Modelling 55 (2012) 1601-1609].
A result of Suzuki type in partial G-metric spaces
2014
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial …
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 generalized metric spaces
2012
Abstract We establish some common fixed point theorems for mappings satisfying a ( ψ , φ ) -weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing 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.
Common fixed point results on quasi-Banach spaces and integral equations
2013
In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.
Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces
2012
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…
Nonlinear contractions involving simulation functions in a metric space with a partial order
2015
Very recently, Khojasteh, Shukla and Radenovic [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a …