Related papers: Using the KKM theorem

The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of…

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with…

Let $A$ be a separable, unital and exact $C^*$-algebra satisfying the universal coefficient theorem. We prove uniqueness theorems up to unitary conjugacy for unital, full and nuclear maps from $A$ into ultraproducts of finite von Neumann…

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…

In this paper, we show the existence of a positive solution of a Hammerstein integral equation under certain conditions on the kernel. We apply the recent Layered Compression-Expansion Fixed Point Theorem. Finally, we provide corollaries to…

We establish a simple and powerful lemma that provides a criterion for sequences in metric spaces to be Cauchy. Using the lemma, it is then easily verified that the Picard iterates $\{T^nx\}$, where $T$ is a contraction or asymptotic…

We review the status of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and the CP-violating phases in the CKM-unitarity triangle. The emphasis in these lecture notes is on $B$-meson physics, though we also review the current status and…

In the present paper, a new type of mappings called perimetric contractions on $k$-polygons is introduced. These contractions can be viewed as a generalization of mappings that contracts perimeters of triangles. A fixed point theorem for…

This work is motivated by problems on simultaneous Diophantine approximation on manifolds, namely, establishing Khintchine and Jarnik type theorems for submanifolds of R^n. These problems have attracted a lot of interest since Kleinbock and…

The study of fixed point ratios is a classical topic in permutation group theory, with a long history stretching back to the origins of the subject in the 19th century. Fixed point ratios arise naturally in many different contexts, finding…

Tanaka (1997) proved a powerful generalization of Friedman's self-embedding theorem that states that given a countable nonstandard model $(\mathcal{M},\mathcal{A})$ of the subsystem $\mathrm{WKL}_{0}$ of second order arithmetic, and any…

In this paper, we study generalized versions of the k-center problem, which involves finding k circles of the smallest possible equal radius that cover a finite set of points in the plane. By utilizing the Minkowski gauge function, we…

In this paper we introduce a new formalism for $K$-theory, called squares $K$-theory. This formalism allows us to simultaneously generalize the usual three-term relation $[B] = [A] + [C]$ for an exact sequence $A \hookrightarrow B…

This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}. The first correction is needed in order to establish the existence of…

The classical Enestrom-Kakeya theorem establishes upper and lower bounds on the zeros of a polynomial with positive coefficients that are explicit functions of those coefficients. We establish a unifying framework that incorporates this…

K-Medoids(KM) is a standard clustering method, used extensively on semi-metric data.Error analyses of KM have traditionally used an in-sample notion of error,which can be far from the true error and suffer from generalization gap. We…

Higher twisted $K$-theory is an extension of twisted $K$-theory introduced by Ulrich Pennig which captures all of the homotopy-theoretic twists of topological $K$-theory in a geometric way. We give an overview of his formulation and key…

We compute the algebraic K-theory of the non-commutative ring k<x_1,...,x_n>/(m^a) when k is a perfect field of positive characteristic and m=(x_1,...,x_n). We express the answer in terms of the truncation poset Witt vectors developed in…

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.

The aim of this paper is to provide characterizations of a Meir-Keeler type mapping and a fixed point theorem for the mapping in a metric space endowed with a transitive relation.