Related papers: An entire function with no fixed points and no inv…
In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further…
It is shown that that for every Darboux function $F$ there is a non-constant continuous function $f$ such that $F+f$ is still Darboux. It is shown to be consistent --- the model used is iterated Sacks forcing --- that for every Darboux…
We study attracting orbits escaping to infinity in natural families of transcendental entire functions. We show that, if an attracting fixed point escapes to infinity while its multiplier tends to one, then the limiting function has a…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
We consider a nonlinear problem $F(\lambda,u)=0$ on infinite-dimensional Banach spaces that correspond to the steady-state bifurcation case. In the literature, it is found again a bifurcation point of the approximate problem…
We extend the classical Lebesgue and Fubini differentiation theorems to functions of several variables, using the notions of joint derivative and joint monotonicity. Our first main result shows that for a function $f$ of bounded variation,…
It is proved that every function of finite Baire index on a separable metric space $K$ is a $D$-function, i.e., a difference of bounded semi-continuous functions on $K$. In fact it is a strong $D$-function, meaning it can be approximated…
We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to…
Our aim is to show that it is impossible to find a bound for the power of the first fixed point of the aleph function.
This paper describes Turing's Halting Problem (HP), and reviews the classic proof that no function exists that can solve HP. The concept of a "Context-Dependent Function" (CDF), whose behavior varies based on seemingly irrelevant changes to…
In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…
A heuristic principle attributed to A. Bloch says that a family of holomorphic functions is likely to be normal if there is no nonconstant entire functions with this property. We discuss this principle and survey recent results that have…
It is solved a problem of construction of separately continuous functions on the product of compacts with a given discontinuity points set. We obtaine the following results. 1. For arbitrary \v{C}ech complete spaces $X$, $Y$ and a separable…
If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend…
We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a…
Sanchez, Viader, Paradis and Carrillo (2016) proved that there exists an increasing continuous singular function $f$ on $[0,1]$ such that the set $A_f$ of points where $f$ has a nonzero finite derivative has Hausdorff dimension 1 in each…
We consider Gomory and Johnson's infinite group model with a single row. Valid inequalities for this model are expressed by valid functions and it has been recently shown that any valid function is dominated by some nonnegative valid…
This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even function on a Riemannian manifold with a pole and proved…
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…
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.