1. On a new class of functional equations satisfied by polynomial functions.
- Author
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Nadhomi, Timothy, Okeke, Chisom Prince, Sablik, Maciej, and Szostok, Tomasz
- Subjects
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POLYNOMIALS , *LINEAR equations , *FUNCTIONAL equations , *MATHEMATICS , *EQUATIONS - Abstract
The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Székelyhidi's result may be generalized to equations where some occurrences of the unknown functions are multiplied by a linear combination of the variables. In this paper we study the equations where two such combinations appear. The simplest nontrivial example of such a case is given by the equation F (x + y) - F (x) - F (y) = y f (x) + x f (y) considered by Fechner and Gselmann (Publ Math Debrecen 80(1–2):143–154, 2012). In the present paper we prove several results concerning the systematic approach to the generalizations of this equation. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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