Related papers: The Fixed Point Property for Posets of Small Width

Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially…

Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are…

This thesis focuses on renormalization of tensor field theories. Its first part considers a quartic tensor model with $O(N)^3$ symmetry and long-range propagator. The existence of a non-perturbative fixed point in any $d$ at large $N$ is…

We study the existence of fixed points for continuous maps $f$ from an $n$-ball $X$ in $\mathbb R^n$ to $\mathbb R^n$ with $n\geq 1$. We show that $f$ has a fixed point if, for some absolute retract $Y\subset\partial X$, $f(Y)\subset X$ and…

Inverse limits, unlike direct limits, can in general be void, [1]. The existence of fixed points for arbitrary mappings $T : X \longrightarrow X$ is conjectured to be equivalent with the fact that related direct limits of all finite…

Suppose that E is a Banach space, {\tau} a topology under which the norm of E becomes {\tau}-lower semicontinuous and S a commuting family of {\tau}-continuous nonexpansive mappings defined on a {\tau}-compact convex subset C of E: It is…

In this paper we first extend from normed spaces to locally convex spaces some characterizations of denting points in convex sets. On the other hand, we also prove that in an infrabarreled locally convex space a point in a convex set is…

Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.

In this paper we present some fixed-figure theorems as a geometric approach to the fixed-point theory when the number of fixed points of a self-mapping is more than one. To do this, we modify the Jleli-Samet type contraction and define new…

The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…

We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.

We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained…

The following natural question arises from Shalom's innovational work (1999, Publ. IHES): "Can we establish an intrinsic criterion to synthesize relative fixed point properties into the whole fixed point property without assuming Bounded…

Our main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs. We conclude by…

Motivated by M. Scharlemann and A. Thompson's definition of thin position of 3-manifolds, we define the width of a handle decomposition a 4-manifold and introduce the notion of thin position of a compact smooth 4-manifold. We determine all…

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…

Posets which are retract of products of chains are characterized by means of two properties: \emph{the chain-gap property} and \emph{the selection property} (Rival and Wille, 1981 \cite {R-W}). Examples of posets with the selection property…

We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…

A famous theorem of Dilworth asserts that any finite poset of width $k$ can be decomposed into $k$ chains. We study the following problem: given a Borel poset $P$ of finite width $k$, is it true that it can be decomposed into $k$ Borel…

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.