Search results for "c space"
showing 10 items of 552 documents
Sobolev Spaces and Quasiconformal Mappings on Metric Spaces
2001
Heinonen and I have recently established a theory of quasiconformal mappings on Ahlfors regular Loewner spaces. These spaces are metric spaces that have sufficiently many rectifiable curves in a sense of good estimates on moduli of curve families. The Loewner condition can be conveniently described in terms of Poincare inequalities for pairs of functions and upper gradients. Here an upper gradient plays the role that the length of the gradient of a smooth function has in the Euclidean setting. For example, the Euclidean spaces and Heisenberg groups and the more general Carnot groups admit the type of a Poincare inequality we need. We describe the basics and discuss the associated Sobolev sp…
On almost Dugundji spaces and dyadic spaces
1994
On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition
2019
In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generaliz…
Solvability of integrodifferential problems via fixed point theory in b-metric spaces
2015
The purpose of this paper is to study the existence of solutions set of integrodifferential problems in Banach spaces. We obtain our results by using fixed point theorems for multivalued mappings, under new contractive conditions, in the setting of complete b-metric spaces. Also, we present a data dependence theorem for the solutions set of fixed point problems.
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.
Removable sets for intrinsic metric and for holomorphic functions
2019
We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every totally disconnected set with finite Hausdorff measure of codimension 1 is metrically removable, which answers a question raised by Hakobyan and Herron. The metrically removable sets are shown to be related to other classes of "thin" sets that appeared in the literature. They are also related to the removability problems for classes of holomorphic functions with restrictions on the derivative.
Generalized F-Contractions on Product of Metric Spaces
2019
Our purpose in this paper is to extend the fixed point results of a &psi
Quasispheres and metric doubling measures
2018
Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking.
Assouad dimension, Nagata dimension, and uniformly close metric tangents
2013
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…
Tripled Fixed Point Results for T-Contractions on Abstract Metric Spaces
2014
In this paper we introduce the notion of T-contraction for tripled fi xed points in abstract metric spaces and obtain some tripled fi xed point theorems which extend and generalize well-known comparable results in the literature. To support our results, we present an example and an application to integral equations.