Report of Meeting. The Fifteenth Katowice-Debrecen Winter Seminar, Będlewo (Poland), January 28–31, 2015
Journal Title: Annales Mathematicae Silesianae - Year 2015, Vol 29, Issue
Abstract
Report of Meeting. The Fifteenth Katowice-Debrecen Winter Seminar, Będlewo (Poland), January 28–31, 2015
A general fixed point theorem for implicit cyclic multi-valued contraction mappings
In this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15],...
Infinite towers of Galois defect extensions of Kaplansky fields
We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers...
Wild primes of a higher degree self-equivalence of a number field
Let $\mathcal{l} > 2$ be a prime number. Let $K$ be a number field containing a unique $\mathcal{l}$-adic prime and assume that its class is an $\mathcal{l}$th power in the class group $C_K$. The main theorem of the pape...
A simple proof of the Polar Decomposition Theorem
In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad...
On the general and measurable solutions of some functional equations
The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these general solutions, the Lebesgue measurable solutions have bee...