Related papers: Convex KKM maps, monotone operators and Minty vari…
We use $KKM$ theorem to prove the existence of a new fixed point theorem for non-expansive mapping:Let M be a bounded closed convex subset of Hilbert space H, and $A:M\rightarrow M$ be a non-expansive mapping, then exists a fixed point of A…
We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings. The main result states that the range of an average of firmly…
The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…
Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…
Incremental models for magnetic vector hysteresis have been developed in previous works in accordance with basic principles of thermodynamics. In this paper, we present an equivalent representation of the associated hysteresis operator in…
We consider convex maps f:R^n -> R^n that are monotone (i.e., that preserve the product ordering of R^n), and nonexpansive for the sup-norm. This includes convex monotone maps that are additively homogeneous (i.e., that commute with the…
We study continuous countably piecewise monotone interval maps, and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our…
In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
Since its introduction over 50 years ago, the concept of Mosco convergence has permeated through diverse areas of mathematics and applied sciences. These include applied analysis, the theory of partial differential equations, numerical…
We prove an abstract criterion that a surjective convolution operator in spaces of analytic functions on convex subsets of the complex plane has a continuous linear right inverse. Considered convex sets have a countable neighborhood basis…
The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
By means of fixed point index theory for multi-valued maps, we provide an analogue of the classical Birkhoff--Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general…
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…
In this note, we study an invariant associated to the zeros of the moment map generated by an action form, the infinitesimal index. This construction will be used to study the compactly supported equivariant cohomology of the zeros of the…
We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for…
We prove the (generalized) principal pivot transform is matrix monotone, in the sense of the L\"owner ordering, under minimal hypotheses. This improves on the recent results of J. E. Pascoe and R. Tully-Doyle, Monotonicity of the principal…
These lectures centered around the Kempf-Ness theorem, which describes the equivalence between notions of quotient in symplectic and algebraic geometry. The text also describes connections to invariant theory, such existence of invariants…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…