Narrow Results

In the spirit of some earlier studies of the authors, we discuss the alienation problem for ∨-additive and multiplicative mappings. This study enables us to answer two questions that were left open in [B. Al Subaiei and N. Jarboui, On the monoid of unital endomorphisms of a Boolean ring, Axioms 10(4) (2021) 305].

We prove the generalized Hyers–Ulam stability of mapping on normed spaces for the following 2-dimensional quadratic functional equation:

The general solutions of a sum form functional equation have been obtained without imposing any regularity condition on any of the mappings appearing in it. Some of these solutions are related to entropies of type (α, β) proposed by Behara and Nath [Information and entropy of countable measurable partitions I, Kybernetika10 (1974) 491–503].

The main purpose of this paper is to describe the structure of a pair of additive mappings that are commuting on a semiprime ring. Furthermore, we prove that the existence of different commuting epimorphisms on a prime ring forces the ring to be commutative. Finally, we characterize additive mappings, which act as homomorphisms or antihomomorphisms on a semiprime ring.