Search

The purpose of this paper is to prove that if on a commutative hypergroup an exponential monomial has the property that the linear subspace of all sine functions in its variety is one dimensional, then this exponential monomial is a linear combination of generalized moment functions. [ABSTRACT FROM AUTHOR]

In the present paper, a general class of linear functional equations is considered and a computer program is described, which determines the exact solutions of systems of equations belonging to this class. [ABSTRACT FROM AUTHOR]

This article has two aims. First, we provide the solution to a problem posed by the author in a previous paper. Second, we consider a problem posed by Kannappan and Kurepa (Aequat Math 4: 163-175, 1970). Our results show that additive functions linked by certain types of functional equations are combinations of linear functions and derivations of various orders. We show that this is not generally the case for the problem of Kannappan and Kurepa, and we modify their problem accordingly. [ABSTRACT FROM AUTHOR]

In this note we provide the solution to a problem posed by the first author in a previous paper. In particular, we prove a result relating the number of nonzero coefficients of a certain functional equation to the order of any derivation satisfying that equation. [ABSTRACT FROM AUTHOR]

We provide a unifying framework for the treatment of equations of the form for additive maps f and integers p, q (1 ≤ k ≤ n). We show how to solve many equations of this type, and we present some open problems. In general our unknown functions map an integral domain of characteristic zero into itself. When negative exponents appear, we restrict our attention to fields of characteristic zero. All of the results could be formulated for integral domains or fields of sufficiently large characteristic as well. [ABSTRACT FROM AUTHOR]