Report of Meeting. The Seventeenth Katowice–Debrecen Winter Seminar Zakopane (Poland) , February 1–4, 2017
Journal Title: Annales Mathematicae Silesianae - Year 2017, Vol 31, Issue
Abstract
Report of Meeting. The Seventeenth Katowice–Debrecen Winter Seminar Zakopane (Poland) , February 1–4, 2017
On a functional equation related to two-sided centralizers
The main aim of this manuscript is to prove the following result. Let $n >2$ be a fixed integer and $R$ be a $k$-torsion free semiprime ring with identity, where $k∈{2,n−1,n}$. Let us assume that for the additive mapping...
An application of the theory of scale of Banach spaces
The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the s...
On Popoviciu-Ionescu functional equation
We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our s...
Alienation of the Jensen, Cauchy and d’Alembert equations
Let $(S,+)$ be a commutative semigroup, $\sigma : S \to S$ be an endomorphism with $\sigma^2 = id$ and let $K$ be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen eq...
Characterizations of rotundity and smoothness by approximate orthogonalities
In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of...