Related papers: Menger Convexity and Hausdorff Metric

We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions on these spaces and refer to it as $W-$convexity.…

We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points…

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…

In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…

The notions of (metric) hypersurface data were introduced in [Mars,2013] as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-riemannian manifolds. In this paper, general geometric properties of…

Because of Minty's classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of basic importance in fixed point theory, monotone operator…

In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of…

We equip the space of Cauchy hypersurfaces in a globally hyperbolic spacetime with a natural Hausdorff-type metric and study its properties, in particular completeness and local compactness, for Lorentzian manifolds and in more general…

Let $\Omega$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $\mathcal{X}$ with dual space $\mathcal{X}^*$. This article presents a hybrid algorithm for finding a common element of the set…

In this paper, using a more generalized inequality instead of triangle inequality, the notion of \theta-metric space is introduced. Some important properties of induced topology by such spaces are presented. Also, Banach and Caristi type…

In this article, we establish a truncated non-integrated defect relation for meromorphic mappings from an $m$-dimensional complete K\"{a}hler manifold into $\mathbb P^n(\mathbb C)$ intersecting $q$ hypersurfaces $Q_1,...,Q_q$ in…

The Hausdorff hyperspace of a metric space consists of all its non-empty bounded closed sets and it is equipped with the Pompeiu--Hausdorff set distance. We present a simpler novel proof that the Hausdorff hyperspace of a complete space is…

For a Tychonoff space $X$ and a family $\lambda$ of subsets of $X$, we denote by $C_{\lambda}(X)$ the space of all real-valued continuous functions on $X$ with the set-open topology. In this paper, we study the Menger and projective Menger…

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due…

This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of $(r,\delta)$-convex spaces, a class of geodesic…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

We show that if $A$ is a closed subset of the Heisenberg group whose vertical projections are nowhere dense, then the complement of $A$ is quasiconvex. In particular, closed sets which are null sets for the cc-Hausdorff $3$-measure have…

We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups…

In 2007 H. Long-Guang and Z. Xian, [H. Long-Guang and Z. Xian, Cone Metric Spaces and Fixed Point Theorems of Contractive Mapping, J. Math. Anal. Appl., 322(2007), 1468-1476], generalized the concept of a metric space, by introducing cone…

We study the positivity of complete intersections of nef classes. We first give a sufficient and necessary characterization on the complete intersection classes which have hard Lefschetz property on a compact complex torus, equivalently, in…