Search results for "convex"
showing 10 items of 389 documents
A note on best approximation in 0-complete partial metric spaces
2014
We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.
Common Fixed Points in a Partially Ordered Partial Metric Space
2013
In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.
On a theorem of Khan in a generalized metric space
2013
Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given.
Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces
2013
Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.
Analytic Extension of Non Quasi - Analytic Whitney Jets of Beurling Type
1998
Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr ≥ 1 for every r ∈ ℕ and defines a non quasi - analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function f on ℝn belonging to the non quasi - analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on ℝ,nF and such that Dαf(x) = Dαg(x) for every α ∈ ℕn0 and x ∈ F.
Vector-valued meromorphic functions
2002
A locally complete locally convex space E satisfies that every weakly meromorphic function defined on an open subset of \( \mathbb{C} \) with values in E is meromorphic if and only if E does not contain a countable product of copies of \( \mathbb{C} \). A characterization of locally complete spaces in the spirit of known characterizations of the (metric) convex compactness property is also given.
On generalized weakly G-contraction mapping in G-metric spaces
2011
In this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.
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.
Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces
1993
In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…
Approximate convex hull of affine iterated function system attractors
2012
International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…