31 problems

P-property conjecture. Under the conditions of Theorem main2, $T$ has the $P$ property. The source further says that it is enough to check whether $T$ satisfies the condition

De Pierro's conjecture. The weak limits satisfy

Kosniowski's conjecture. If $M^{2n}$ is not a boundary, then the number of fixed points is greater than $f(n)$. Kosniowski conjectured that the candidate function is

Index-bound conjecture. One has

Let $m$ agents and $n$ goods be given, with valuation parameters $v_{\ell i}$ and $V=\sum_{\ell,i}v_{\ell i}$. Let $\epsilon>0$ be arbitrarily small and assume $V\leq\epsilon$. Let…

Reflexive-space fixed point conjecture. Every reflexive Banach space has the fixed point property for nonexpansive maps. Equivalently, if $X$ is reflexive and $C\subset X$ is close…

Malkiewich–Ponto's conjecture. The fiberwise Fuller trace

Austin's conjecture. If $\{f_1,\ldots,f_r\}$ is a pairwise commuting family of $\lambda$-contractions on $X$, then the maps have a common fixed point; that is, there exists…

Let $M$ be a closed smooth manifold, let $f:M\to M$ be a self-map, and let $\ell_n(f)$ lie in the direct sum $\bigoplus_{k\mid n}\mathbb{Z}[\pi_1(M)_{\rho,k}]$, where…

Let $G$ act on a closed smooth manifold $M$, let $f:M\to M$ be a $G$-equivariant map, and let $\ell_G(f)$ be the Klein–Williams invariant. For each conjugacy class of subgroups $H$…

Let $A[D_5]$ be the Artin group of spherical type $D_5$, and let $Z(A[D_5])$ denote its center. The $D_5$ property $R_\infty$ conjecture. The Artin group $A[D_5]$ and its central q…

Let $f:\mathbb R^2\rightarrow\mathbb R^2$ be a homeomorphism, and suppose that every orbit of $f$ is bounded. Bounded orbit conjecture. Then $f$ has a fixed point. This conjecture…

Fixed-point characterization. The following conditions are equivalent: (i) $F$ has a fixed point in every nonempty spherically complete subspace of $M$; and (ii) the displayed ineq…

Dimension-bound conjecture. The dimension of $M$ is bounded above by a function of $k$; more precisely,

Let ${\mathbb{T}}^n$ be the $n$-torus, let $f:{\mathbb{T}}^n\to{\mathbb{T}}^n$ be a map, and let $\tau$ be a free involution of ${\mathbb{T}}^n$. Nielsen–Borsuk–Ulam dichotomy conj…

Let $X$ be a contractible digital image and let $f:X\longrightarrow X$ be a continuous mapping. Here, $HFS(f,f)$ denotes the homotopic fixed point set for the pair $(f,f)$, $S(f)$…

For each $n$, let $y_n$ be the sequence-generated root and define … This is the Lipschitz constant in the referenced formula. Contraction conjecture. It is always possible to choos…

Let $n_1,\ldots,n_k$ be distinct positive integers, let $n=n_1+\cdots+n_k$, and for $\mathbb{F}\in\{\mathbb{R},\mathbb{C}\}$ define … where $U_{\mathbb{R}}(n)=O(n)$ and…

The contractive-grid conjecture. Every such grid contains a 1-way Cauchy sequence. The conjecture is introduced as a formulation capturing the essence of Austin's common fixed poin…

Let $E$ be a smooth and uniformly convex Banach space of dimension two. Let $K\subseteq E$ be nonempty, closed, bounded, and convex, and let $f\colon K\to E$ be nonexpansive with…

Let $E$ be a uniformly convex, smooth, computable Banach space of dimension two, and let $K\subseteq E$ be bounded, convex, and located, meaning that its distance function is compu…

Let $C$ be a bounded convex domain in $\mathbb{R\mathrm{^{N}}}$ equipped with Hilbert's metric $d$, and let $f:C\rightarrow C$ be a 1-Lipschitz map. Nussbaum–Vandehey conjecture. E…

Limiting lower-bound conjecture. The sequence of lower bounds satisfies

Limiting $V_n$-density conjecture. The limiting density is

Bordered-manifold Hopf brushing conjecture. Let $W$ be a compact bordered manifold (first $C^{\infty}$ and then $C^0$). Assume that $c7(W)=0$, and when $W$ is odd-dimensional that…