Search results for "partially ordered set"
showing 10 items of 23 documents
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].
Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces
2011
Abstract In this paper, we establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to Ciric (2009) [3] . An example is given to illustrate the usability of our results.
Set-valued mappings in partially ordered fuzzy metric spaces
2014
Abstract In this paper, we provide coincidence point and fixed point theorems satisfying an implicit relation, which extends and generalizes the result of Gregori and Sapena, for set-valued mappings in complete partially ordered fuzzy metric spaces. Also we prove a fixed point theorem for set-valued mappings on complete partially ordered fuzzy metric spaces which generalizes results of Mihet and Tirado. MSC:54E40, 54E35, 54H25.
Meir-Keeler Type Contractions for Tripled Fixed Points
2012
Abstract In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.
Spaces of typen on partially ordered sets
1989
This paper contains a generalized approach to incidence geometry on partially ordered sets. A difference to the usual geometrical concepts is that points may have different size. Our main result states that a large class of spaces allows lattice theoretic characterizations. Especially, a generalized version of the Veblen-Young axiom of projective geometry has a lattice theoretic equivalent, called then-generation property (which is a generalization of the ‘Verbindungssatz’). Modularity and distributivity of a lattice of subspaces are reflected in the underlying space. Finally we give specializations and examples.
Coupled coincidence points for compatible mappings satisfying mixed monotone property
2012
We establish coupled coincidence and coupled fixed point results for a pair of mappings satisfying a compatibility hypothesis in partially ordered metric spaces. An example is given to illustrate our obtained results.
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations
2012
In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.
Holographic duals of 6d RG flows
2018
A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer $N$, an ADE group $G$, and two nilpotent elements $\mu_\mathrm{L,R}$ in $G$. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for $G=\mathrm{SU}(k)$, where AdS$_7$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two $\mathrm{SU}(k)$ non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS$_7$ vacua, determined by two nilpotent elements, which are naturally …
Coupled fixed point, F-invariant set and fixed point of N-order
2010
In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of $F$-invariant set. We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature.
Patterns in words and languages
2004
AbstractA word p, over the alphabet of variables E, is a pattern of a word w over A if there exists a non-erasing morphism h from E∗ to A∗ such that h(p)=w. If we take E=A, given two words u,v∈A∗, we write u⩽v if u is a pattern of v. The restriction of ⩽ to aA∗, where A is the binary alphabet {a,b}, is a partial order relation. We introduce, given a word v, the set P(v) of all words u such that u⩽v. P(v), with the relation ⩽, is a poset and it is called the pattern poset of v. The first part of the paper is devoted to investigate the relationships between the structure of the poset P(v) and the combinatorial properties of the word v. In the last section, for a given language L, we consider …