Search results for " metric space"
showing 8 items of 168 documents
Coupled fixed-point results for T-contractions on cone metric spaces with applications
2015
The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., “Remarks on “Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings”,” Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.
Coupled fixed point theorems for symmetric (phi,psi)-weakly contractive mappings in ordered partial metric spaces
2013
We establish some coupled fixed point theorems for symmetric (phi,chi)-weakly contractive mappings in ordered partial metric spaces. Some recent results of Berinde (Nonlinear Anal. 74 (2011), 7347-7355; Nonlinear Anal. 75 (2012), 3218-3228) and many others are extended and generalized to the class of ordered partial metric spaces.
On modified α-ϕ-fuzzy contractive mappings and an application to integral equations
2016
Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.
Mappings of finite distortion between metric measure spaces
2015
We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a ( 1 , 1 ) (1,1) -Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n n -manifolds of type A A has zero Hausdorff n n -measure.
Some critical remarks on the paper “A note on the metrizability of tvs-cone metric spaces” / Некоторые критические замечания о работе «Заметки о метр…
2018
This short and concise note provides a detailed exposition of the approach and results established by (Lin et al, 2015, pp.271-279). We show that the obtained results are not particularly surprising and new. Namely, using an old result due to K. Deimling it is indicated that tvs-cone metric spaces over solid cones are actually cone metric spaces over normal solid cones. Hence, there are only cone metric spaces over normal solid cones or over normal non-solid cones. One question still unanswered is whether an ordered topological vector space with a non-normal non-solid cone exists. / В представленных, в данной статье, заметках приведен подробный обзор методов и полученных результатов исследо…
On multivalued weakly Picard operators in partial Hausdorff metric spaces
2015
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
The Hajłasz Capacity Density Condition is Self-improving
2022
We prove a self-improvement property of a capacity density condition for a nonlocal Hajlasz gradient in complete geodesic spaces with a doubling measure. The proof relates the capacity density condition with boundary Poincare inequalities, adapts Keith-Zhong techniques for establishing local Hardy inequalities and applies Koskela-Zhong arguments for proving self-improvement properties of local Hardy inequalities. This leads to a characterization of the Hajlasz capacity density condition in terms of a strict upper bound on the upper Assouad codimension of the underlying set, which shows the self-improvement property of the Hajlasz capacity density condition. Open Access funding provided than…
Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces
2011
The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.