In this paper we consider stability in the Ulam-Hyers sense, and in other similar senses, for the five equivalent definitions of one-dimensional dynamical systems. [ABSTRACT FROM AUTHOR]
The issue of distributivity of aggregation operations is crucial for many different areas such as utility theory and integration theory. Of special interest are aggregation operations with annihilator. This paper is focused on the problem of distributivity for some so called associative, commutative aggregation operations with annihilator a, known as associative a-CAOA, and uninorms. The full characterization of distributive pairs for T-uninorms, S-uninorms and bi-uninorms is given.
Pure mathematics, Dirac measure, General Mathematics, 39B22, 62E10, Uniform distribution, 010103 numerical & computational mathematics, Characterization (mathematics), 01 natural sciences, symbols.namesake, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Cauchy distribution, Discrete Mathematics and Combinatorics, Inverse trigonometric functions, 0101 mathematics, Borel measure, Mathematics, Applied Mathematics, 010102 general mathematics, Probability (math.PR), Probabilistic logic, Functional equations, Function (mathematics), Mathematics - Classical Analysis and ODEs, symbols, Measurability, Mathematics - Probability
Abstract
This paper deals with functional equations in the form of $f(x) + g(y) = h(x,y)$ where $h$ is given and $f$ and $g$ are unknown. We will show that if $h$ is a Borel measurable function associated with characterizations of the uniform or Cauchy distributions, then there is no measurable solutions of the equation. Our proof uses a characterization of the Dirac measure and it is also applicable to the arctan equation., Comment: 7 pages, to appear in Aequationes mathematicae
Published
2021
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