Search results for "metric spaces"
showing 10 items of 49 documents
Nonlinear psi-quasi-contractions of Ciric-type in partial metric spaces
2012
In this paper we obtain results of fixed and common fixed points for self-mappings satisfying a nonlinear contractive condition of Ciric-type in the framework of partial metric spaces. We also prove results of fixed point for self-mappings satisfying an ordered nonlinear contractive condition in the setting of ordered partial metric spaces.
Fixed point results for $GP_(Λ,Θ)$-contractive mappings
2014
In this paper, we introduce new notions of GP-metric space and $GP_(Λ,Θ)$-contractive mapping and then prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach contraction principle to GP-metric spaces. An example shows the usefulness of our results.
On generalized weakly G-contraction mapping in G-metric spaces
2011
AbstractIn 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.
Fixed point theorems in generalized partially orderedG-metric spaces
2010
In this paper, we consider the concept of a $\Omega$-distance on a complete partially ordered G-metric space and prove some fixed point theorems.
Best Proximity Points for Some Classes of Proximal Contractions
2013
Given a self-mapping g: A → A and a non-self-mapping T: A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g-best proximity point, which satisfies d g x, T x = d A, B. In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-s…
Higher integrability and stability of (p,q)-quasiminimizers
2023
Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a $(p,q)$-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents $p$ and $q$. The setting is a doubling metric measure space supporting a Poincar\'e inequality.
Tensorization of quasi-Hilbertian Sobolev spaces
2022
The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space $X\times Y$ can be determined from its factors. We show that two natural descriptions of the Sobolev space from the literature coincide, $W^{1,2}(X\times Y)=J^{1,2}(X,Y)$, thus settling the tensorization problem for Sobolev spaces in the case $p=2$, when $X$ and $Y$ are infinitesimally quasi-Hilbertian, i.e. the Sobolev space $W^{1,2}$ admits an equivalent renorming by a Dirichlet form. This class includes in particular metric measure spaces $X,Y$ of finite Hausdorff dimension as well as infinitesimally Hilbertian spaces. More generally for $p\in (1,\infty)$ we…
Approximation of fixed points of multifunctions in partial metric spaces
2013
Recently, Reich and Zaslavski [S. Reich and A.J. Zaslavski, Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 518243, 10pages] have studied a new inexact iterative scheme for fixed points ofcontractive multifunctions. In this paper, using the partial Hausdorffmetric introduced by Aydi et al., we prove an analogous to a resultof Reich and Zaslavski for contractive multifunctions in the setting ofpartial metric spaces. An example is given to illustrate our result. 
A Remark on an Overdetermined Problem in Riemannian Geometry
2016
Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let \(\varOmega \subset M\) be a bounded domain, with \(O \in \varOmega \), and consider the problem \(\varDelta _p u = -1\ \mathrm{in}\ \varOmega \) with \(u=0\ \mathrm{on}\ \partial \varOmega \), where \(\varDelta _p\) is the p-Laplacian of g. We prove that if the normal derivative \(\partial _{\nu }u\) of u along the boundary of \(\varOmega \) is a function of d satisfying suitable conditions, then \(\varOmega \) must be a geodesic ball. In particular, our result applies to open balls of \(\mathbb {R}^n\) equipped with a rotationally symmetric metr…
Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral
2021
Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincar\'{e} inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H\"{o}lder continuous and they satisfy Harnack inequality, the strong maximum principle, and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H\"older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we cons…