# zbMATH — the first resource for mathematics

A few remarks on almost $$C$$-polynomial functions. (English) Zbl 1150.39328
Summary: We give some sufficient conditions for a function transforming a commutative semigroup to a commutative group to be a polynomial function. Some stability results are also given.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges
Full Text:
##### References:
 [1] ALBERT M. A.-BAKER J. A.: Functions with bounded n-th differences. Ann. Polon. Math. 43 (1983), 93-103. · Zbl 0436.39005 [2] DJOKOVIC D. Z.: A representation theorem for $$(X_1 - 1)(X_2 - 1) \cdots (X_n - 1)$$ and its applications. Ann. Polon. Math. 22 (1969), 189-198. [3] KOMINEK Z.: Note on polynomial functions. Ann. Math. Sil. 7 (1993), 7-15. · Zbl 0805.39010 [4] KUCZMA M.: An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality. Pr. Nauk. Uniw. SI. Katow. 489, Wydawn. Uniw. Slaskiego/Panstwowe Wydawnictwo Naukowe, Katowice/Warszawa-Krakow-Katowice, 1985. · Zbl 0555.39004 [5] MAZUR S.-ORLICZ W.: Grundlegende Eigenschaften der polynomischen Operationen I. Studia Math. 5 (1934), 50-68. · Zbl 0013.21002 · eudml:218123
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.