Related papers: Lifting classes for the fixed point theory of $n$-…

In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et…

We give an explicit presentation of a family of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero that constitute all liftings of Nichols algebras of diagonal Cartan type $B_{3}$ over a…

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand the existing framework, so that it will apply to not…

Let $X$ be a metric space. Recently in~[1] it was considered a new type of mappings $T\colon X\to X$ which can be characterized as mappings contracting perimeters of triangles. These mappings are defined by the condition based on the…

We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

Fixpoint operators are tools to reason on recursive programs and data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. A…

We introduce characteristic functions for certain contractive liftings of row contractions. These are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model. The most important…

In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…

For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism f is equal to the number of finite-dimensional fixed points of the induced map f^…

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

We give an axiomatic characterization of the fixed point index of an $n$-valued map. For $n$-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting…

We consider a closed convex set $C$ in a separable, infinite-dimensional Hilbert space and endow the set $\mathcal{N}(C)$ of nonexpansive self-mappings on $C$ with the topology of pointwise convergence. We introduce the notion of a somewhat…

We prove a uniform version of the Dynamical Mordell-Lang Conjecture for \'etale maps; also, we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary endomorphism of a quasiprojective variety defined…

For a Hausdorff space $X$, we exhibit an unexpected connection between the sectional number of the Fadell-Neuwirth fibration $\pi_{2,1}^X:F(X,2)\to X$, and the fixed point property (FPP) for self-maps on $X$. Explicitly, we demonstrate that…

The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to…

In this paper, we study the existence of common fixed points of family of multivalued mappings satisfying generalized F-contractive conditions in ordered metric spaces. These results establish some of the general common fixed point theorems…

We show that branched coverings of surfaces of large enough genus arise as characteristic maps of braided surfaces that is, lift to embeddings in the product of the surface with $\mathbb R^2$. This result is nontrivial already for…

Let $X$ be a smooth hypersurface of dimension $n\geq 1$ and degree $d\geq 3$ in the projective space given as the zero set of a homogeneous form $F$. If $(n,d)\neq (1,3), (2,4)$ it is well known that every automorphism of $X$ extends to an…

We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete,…